Volume 55, Issue 1

In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals.

We study the dynamics of a meromorphic perturbation of the family λ sin z \lambda \sin z by adding a pole at zero and a parameter μ \mu , that is, f λ , μ ( z ) = λ sin z + μ / z {f}_{\lambda ,\mu }\left(z)=\lambda \sin z+\mu \hspace{-0.08em}\text{/}\hspace{-0.08em}z , where λ , μ ∈ C ⧹ { 0 } \lambda ,\mu \in {\mathbb{C}}\hspace{-0.16em}\setminus \hspace{-0.16em}\left\{0\right\} . We study some geometrical properties of f λ , μ {f}_{\lambda ,\mu } and prove that the imaginary axis is invariant under f n {f}^{n} and belongs to the Julia set when ∣ λ ∣ ≥ 1 | \lambda | \ge 1 . We give a set of parameters ( λ , μ ) \left(\lambda ,\mu ) , such that the Fatou set of f λ , μ {f}_{\lambda ,\mu } has two super-attracting domains. If λ = 1 \lambda =1 and μ ∈ ( 0 , 2 ) \mu \in \left(0,2) , the Fatou set of f 1 , μ {f}_{1,\mu } has two attracting domains. Also, we give parameters λ , μ \lambda ,\mu such that ± π / 2 \pm \pi \hspace{-0.08em}\text{/}\hspace{-0.08em}2 are fixed points of f λ , μ {f}_{\lambda ,\mu } and the Fatou set of f λ , μ {f}_{\lambda ,\mu } contains attracting domains, parabolic domains, and Siegel discs, we present examples of these domains. This paper closes with an example of f λ , μ {f}_{\lambda ,\mu } , where the Fatou set contains two types of domains, for λ , μ \lambda ,\mu given.

In this article, we study the asymptotic behavior of even-order neutral delay differential equation ( a ⋅ ( u + ρ ⋅ u ∘ τ ) ( n − 1 ) ) ′ ( ℓ ) + h ( ℓ ) u ( g ( ℓ ) ) = 0 , ℓ ≥ ℓ 0 , {(a\cdot {(u+\rho \cdot u\circ \tau )}^{(n-1)})}^{^{\prime} }(\ell )+h(\ell )u(g(\ell ))=0,\hspace{1.0em}\ell \ge {\ell }_{0}, where n ≥ 4 n\ge 4 , and in noncanonical case, that is, ∫ ∞ a − 1 ( s ) d s < ∞ . \mathop{\int }\limits^{\infty }{a}^{-1}\left(s){\rm{d}}s\lt \infty . To the best of our knowledge, most of the previous studies were concerned only with the study of n n -order neutral equations in canonical case. By using comparison principle and Riccati transformation technique, we obtain new criteria which ensure that every solution of the studied equation is either oscillatory or converges to zero. Examples are presented to illustrate our new results.

The study of biofilm formation is becoming increasingly important. Microbes that produce biofilms have complicated impact on medical implants. In this paper, we construct an unconditionally positive non-standard finite difference scheme for a mathematical model of biofilm formation on a medical implant. The unknowns in many applications reflect values that cannot be negative, such as chemical component concentrations or population numbers. The model employed here uses the bistable Allen-Cahn partial differential equation, which is a generalization of Fisher’s equation. We study consistency and convergence of the scheme constructed. We compare the performance of our scheme with a classical finite difference scheme using four numerical experiments. The technique used in the construction of unconditionally positive method in this study can be applied to other areas of mathematical biology and sciences. The results here elaborate the benefits of the non-standard approximations over the classical approximations in practical applications.

This paper introduces three different normalization associated with the second and third q -Bessel-Struve functions. We use Hadamard factorizations to determine the radii of starlike and convexity of these functions.

The bank run phenomenon, mostly due to rumor spread about the financial health of given financial institutions, is prejudicious to the stability of financial systems. In this paper, by using the epidemiological approach, we propose a nonlinear model for describing the impact of rumor on the banking crisis spread. We establish conditions under which the crisis dies out or remains permanent. We also solve an optimal control problem focusing on the minimization, at the lowest cost, of the number of stressed banks, as well as the number of banks undergoing the restructuring process. Numerical simulations are performed to illustrate theoretical results obtained.

We show that, in L p ( 0 , ∞ ) {L}_{p}\left(0,\infty ) ( 1 ≤ p < ∞ 1\le p\lt \infty ), bounded weighted translations as well as their unbounded counterparts are chaotic linear operators. We also extend the unbounded case to C 0 [ 0 , ∞ ) {C}_{0}{[}0,\infty ) and describe the spectra of the weighted translations provided the underlying spaces are complex.

The present paper deals with an extension of approximation properties of generalized sampling series to weighted spaces of functions. A pointwise and uniform convergence theorem for the series is proved for functions belonging to weighted spaces. A rate of convergence by means of weighted moduli of continuity is presented and a quantitative Voronovskaja-type theorem is obtained.

We develop a method for calculating the persistence landscapes of affine fractals using the parameters of the corresponding transformations. Given an iterated function system of affine transformations that satisfies a certain compatibility condition, we prove that there exists an affine transformation acting on the space of persistence landscapes, which intertwines the action of the iterated function system. This latter affine transformation is a strict contraction and its unique fixed point is the persistence landscape of the affine fractal. We present several examples of the theory as well as confirm the main results through simulations.

In this paper, we propose and study a new inertial iterative algorithm with self-adaptive step size for approximating a common solution of finite family of split monotone variational inclusion problems and fixed point problem of a nonexpansive mapping between a Banach space and a Hilbert space. This method combines the inertial technique with viscosity method and self-adaptive step size for solving the common solution problem. We prove a strong convergence result for the proposed method under some mild conditions. Moreover, we apply our result to study the split feasibility problem and split minimization problem. Finally, we provide some numerical experiments to demonstrate the efficiency of our method in comparison with some well-known methods in the literature. Our method does not require prior knowledge or estimate of the operator norm, which makes it easily implementable unlike so many other methods in the literature, which require prior knowledge of the operator norm for their implementation.

Let S S be an inverse semigroup with the set of idempotents E E . In this article, we find necessary and sufficient conditions for the weighted semigroup algebra l 1 ( S , ω ) {l}^{1}\left(S,\omega ) to be module approximately amenable (contractible) and module character amenable (as l 1 ( E ) {l}^{1}\left(E) -module).

Quite recently, a new minimal structure m H ⋆ {m}_{H}^{\star } and an m n mn - ℋ g {{\mathcal{ {\mathcal H} }}}_{g} -closed set have been introduced in a previous study [T. Noiri and V. Popa, Closed sets in hereditary bi m-spaces , Questions Answers General Topol. 38 (2020), 133–142] by using two minimal structures m , n n and a hereditary class ℋ {\mathcal{ {\mathcal H} }} . In this paper, we introduce and investigate the notions of ( m , n ) \left(m,n) - ℋ g ⋆ {{\mathcal{ {\mathcal H} }}}_{g}^{\star } -regularity and ( m , n ) \left(m,n) - ℋ g ⋆ {{\mathcal{ {\mathcal H} }}}_{g}^{\star } -normality in a hereditary bi m -space ( X , m , n , ℋ ) \left(X,m,n,{\mathcal{ {\mathcal H} }}) .

This paper is devoted to the existence of solutions and the multiplicity of positive solutions of an initial-boundary value problem for a nonlinear first-order differential system with nonlocal conditions. The main tool is the fixed-point theorem in which we construct the novel representation of the associated Green’s functions with useful properties and define a cone in the Banach space suitably. Some examples are also given to demonstrate the validity of the main results.

The primary objective of this study is to develop two new proximal-type algorithms for solving equilibrium problems in real Hilbert space. Both new algorithms are analogous to the well-known two-step extragradient algorithm for solving the variational inequality problem in Hilbert spaces. The proposed iterative algorithms use a new step size rule based on local bifunction information instead of the line search technique. Two weak convergence theorems for both algorithms are well-established by letting mild conditions. The main results are used to solve the fixed point and variational inequality problems. Finally, we present several computational experiments to demonstrate the efficiency and effectiveness of the proposed algorithms.

Let Y Y be a random real response, which is subject to right censoring by another random variable C C . In this paper, we study the nonparametric local linear estimation of the conditional density of a scalar response variable and when the covariable takes values in a semi-metric space. Our main aim is to prove under some regularity conditions both the pointwise and the uniform almost-sure consistencies with convergence rates of the conditional density estimator related by this estimation procedure.

Let G G be an abelian group with identity e e . Let R R be a G G -graded commutative ring and M M a graded R R -module. In this paper, we will obtain some results concerning the graded generalized 2-absorbing submodules and their homogeneous components. Special attention has been paid, when graded rings are graded gr-Noetherian, to find extra properties of these graded submodules.

In this article, some inclusion sets for eigenvalues of a matrix in the linear response eigenvalue problem (LREP) are established. It is proved that the inclusion sets are tighter than the Geršgorin-type sets. A numerical experiment shows the effectiveness of our new results.

It is a well-known fact that inclusion and pseudo-order relations are two different concepts which are defined on the interval spaces, and we can define different types of convexities with the help of both relations. By means of pseudo-order relation, the present article deals with the new notions of convex functions which are known as left and right log- s s -convex interval-valued functions (IVFs) in the second sense. The main motivation of this study is to present new inequalities for left and right log- s s -convex-IVFs. Therefore, we establish some new Jensen-type, Hermite-Hadamard ( HH )-type, and Hermite-Hadamard-Fejér ( HH -Fejér)-type inequalities for this kind of IVF, which generalize some known results. To strengthen our main results, we provide nontrivial examples of left and right log- s s -convex IVFs.

Sarsak [M. S. Sarsak, On some properties of generalized open sets in generalized topological spaces , Demonstr. Math. 46 (2013), no. 2, 415–427] studied some properties of generalized open sets in generalized topological spaces (GTSs); the primary purpose of this article is to investigate more properties of generalized open sets in GTSs. We mainly study the behaviours of regular closed sets, semi-open sets, regular semi-open sets, preopen sets, and β \beta -open sets in GTSs analogous to their behaviours in topological spaces.

The purpose of this article is to study and analyse a new extragradient-type algorithm with an inertial extrapolation step for solving split fixed-point problems for demicontractive mapping, equilibrium problem, and pseudomonotone variational inequality problem in real Hilbert spaces. One of the advantages of the proposed algorithm is that a strong convergence result is achieved without a prior estimate of the Lipschitz constant of the cost operator, which is very difficult to find. In addition, the stepsize is generated at each iteration by some simple computations, which allows it to be easily implemented without the prior knowledge of the Lipschitz constant of the cost operator. Some numerical experiments are reported to show the performance and behaviour of the sequence generated by our algorithm. The obtained results in this article extend and improve many related recent results in this direction in the literature.

We establish an accurate and efficient scheme with four-order accuracy for solving three-dimensional (3D) acoustic wave equation. First, the local one-dimensional method is used to transfer the 3D wave equation into three one-dimensional wave equations. Then, a new scheme is obtained by the Padé formulas for computation of spatial second derivatives and the correction of the truncation error remainder for discretization of temporal second derivative. It is compact and can be solved directly by the Thomas algorithm. Subsequently, the Fourier analysis method and the Lax equivalence theorem are employed to prove the stability and convergence of the present scheme, which shows that it is conditionally stable and convergent, and the stability condition is superior to that of most existing numerical methods of equivalent order of accuracy in the literature. It allows us to reduce computational cost with relatively large time step lengths. Finally, numerical examples have demonstrated high accuracy, stability, and efficiency of our method.

In this work, we study the weighted Kirchhoff problem − g ∫ B σ ( x ) ∣ ∇ u ∣ N d x div ( σ ( x ) ∣ ∇ u ∣ N − 2 ∇ u ) = f ( x , u ) in B , u > 0 in B , u = 0 on ∂ B , \left\{\begin{array}{ll}-g\left(\mathop{\displaystyle \int }\limits_{B}\sigma \left(x)| \nabla u\hspace{-0.25em}{| }^{N}{\rm{d}}x\right){\rm{div}}\left(\sigma \left(x)| \nabla u\hspace{-0.25em}{| }^{N-2}\nabla u)=f\left(x,u)& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}B,\\ u\gt 0& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}B,\\ u=0& \hspace{0.1em}\text{on}\hspace{0.1em}\hspace{0.33em}\partial B,\end{array}\right. where B B is the unit ball of R N {{\mathbb{R}}}^{N} , σ ( x ) = log e ∣ x ∣ N − 1 \sigma \left(x)={\left(\log \left(\frac{e}{| x| }\right)\right)}^{N-1} , the singular logarithm weight in the Trudinger-Moser embedding, and g g is a continuous positive function on R + {{\mathbb{R}}}^{+} . The nonlinearity is critical or subcritical growth in view of Trudinger-Moser inequalities. We first obtain the existence of a solution in the subcritical exponential growth case with positive energy by using minimax techniques combined with the Trudinger-Moser inequality. In the critical case, the associated energy does not satisfy the condition of compactness. We provide a new condition for growth, and we stress its importance to check the compactness level.

In this article, motivated by the works of Ali Akbar and Elahe Shahrosvand [ Split equality common null point problem for Bregman quasi-nonexpansive mappings , Filomat 32 (2018), no. 11, 3917–3932], Eskandani et al. [ A hybrid extragradient method for solving pseudomonotone equilibrium problem using Bregman distance , J. Fixed Point Theory Appl. 20 (2018), 132], B. Ali and M. H. Harbau [ Convergence theorems for Bregman K-mappings and mixed equilibrium problems in reflexive Banach spaces , J. Funct. Spaces (2016) Article ID 5161682, 18 pages], and some other related results in the literature, we introduce a hybrid extragradient iterative algorithm that employs a Bregman distance approach for approximating a split feasibility problem for a finite family of equilibrium problems involving pseudomonotone bifunctions and fixed point problems for a finite family of Bregman quasi-asymptotically nonexpansive mappings using the concept of Bregman K-mapping in reflexive Banach spaces. Using our iterative algorithm, we state and prove a strong convergence result for approximating a common solution to the aforementioned problems. Furthermore, we give an application of our main result to variational inequalities and also report a numerical example to illustrate the convergence of our method. The result presented in this article extends and complements many related results in the literature.

With the help of the Nevanlinna theory of meromorphic functions, the purpose of this article is to describe the existence and the forms of transcendental entire and meromorphic solutions for several systems of the quadratic trinomial functional equations: f ( z ) 2 + 2 α f ( z ) g ( z + c ) + g ( z + c ) 2 = 1 , g ( z ) 2 + 2 α g ( z ) f ( z + c ) + f ( z + c ) 2 = 1 , \left\{\begin{array}{l}f{\left(z)}^{2}+2\alpha f\left(z)g\left(z+c)+g{\left(z+c)}^{2}=1,\\ g{\left(z)}^{2}+2\alpha g\left(z)f\left(z+c)+f{\left(z+c)}^{2}=1,\end{array}\right. f ( z + c ) 2 + 2 α f ( z + c ) g ′ ( z ) + g ′ ( z ) 2 = 1 , g ( z + c ) 2 + 2 α g ( z + c ) f ′ ( z ) + f ′ ( z ) 2 = 1 , \left\{\begin{array}{l}f{\left(z+c)}^{2}+2\alpha f\left(z+c)g^{\prime} \left(z)+g^{\prime} {\left(z)}^{2}=1,\\ g{\left(z+c)}^{2}+2\alpha g\left(z+c)f^{\prime} \left(z)+f^{\prime} {\left(z)}^{2}=1,\end{array}\right. and f ( z + c ) 2 + 2 α f ( z + c ) g ″ ( z ) + g ″ ( z ) 2 = 1 , g ( z + c ) 2 + 2 α g ( z + c ) f ″ ( z ) + f ″ ( z ) 2 = 1 . \left\{\begin{array}{l}f{\left(z+c)}^{2}+2\alpha f\left(z+c){g}^{^{\prime\prime} }\left(z)+{g}^{^{\prime\prime} }{\left(z)}^{2}=1,\\ g{\left(z+c)}^{2}+2\alpha g\left(z+c){f}^{^{\prime\prime} }\left(z)+{f}^{^{\prime\prime} }{\left(z)}^{2}=1.\end{array}\right. We obtain a series of results on the forms of the entire solutions with finite order for such systems, which are some improvements and generalizations of the previous theorems given by Gao et al. Moreover, we provide some examples to explain the existence and forms of solutions for such systems in each case.

Let A Φ ( K ) {{\mathbb{A}}}_{\Phi }\left({\bf{K}}) be the Banach algebra of bounded Φ \Phi -variation functions defined on a compact set K {\bf{K}} in the complex plane, h h a function defined on K {\bf{K}} , and M h {M}_{h} a multiplication operator induced by h h . In this article, we determine the conditions that h h must satisfy for M h {M}_{h} to be an operator that has closed range, finite rank or is compact. We also characterize the conditions that h h must satisfy for M h {M}_{h} to be a Fredholm operator.

The modified orthogonal frame is an important tool to study analytic space curves whose curvatures have discrete zero points. In this article, by using the modified orthogonal frame, Mannheim curves and their partner curves are investigated in Minkowski 3-space. Some characterizations according to the curvatures and torsions of the curves are given. Finally, some relations under the conditions for Mannheim curves and their partner curves to be generalized helices are presented. All the possible cases for the partner curves to be spacelike and timelike are considered in the whole of the article.

A square complex matrix A A is said to be group invertible if there exists a matrix X X such that A X A = A AXA=A , X A X = X XAX=X , and A X = X A AX=XA hold, and such a matrix X X is called the group inverse of A A . The group invertibility of a matrix is one of the fundamental concepts in the theory of generalized inverses, while group inverses of matrices have many essential applications in matrix theory and other disciplines. The purpose of this article is to reconsider the characterization problem of the group invertibility of a matrix, as well as the constructions of various algebraic equalities in relation to group invertible matrices. The coverage includes collecting and establishing a family of existing and new necessary and sufficient conditions for a matrix to be group invertible and giving many algebraic matrix equalities that involve Moore-Penrose inverses and group inverses of matrices through the skillful use of a series of highly selective formulas and facts about ranks, ranges, and generalized inverses of matrices, as well as block matrix operations.

In this article, Phillips-type Bernstein operators ( ℬ m , q t F ) ( t , s ) ({{\mathcal{ {\mathcal B} }}}_{m,q}^{t}F)\left(t,s) and ( ℬ n , q s F ) ( t , s ) ({{\mathcal{ {\mathcal B} }}}_{n,q}^{s}F)\left(t,s) , their products, and Boolean sum based on q -integer have been studied on a triangle with all curved sides. Furthermore, convergence of iterates of these operators have been analyzed using the weakly Picard operators technique and the contraction principle.

Recently, electricity consumption forecasting has attracted much research due to its importance in our daily life as well as in economic activities. This process is seen as one of the ways to manage future electricity needs, including anticipating the supply-demand balance, especially at peak times, and helping the customer make real-time decisions about their consumption. Therefore, based on statistical techniques (ST) and/or artificial intelligence (AI), many forecasting models have been developed in the literature, but unfortunately, in addition to poor choice of the appropriate model, time series datasets were used directly without being seriously analyzed. In this article, we have proposed an efficient electricity consumption prediction model that takes into account the shortcomings mentioned earlier. Therefore, the database was analyzed to address all anomalies such as non-numeric values, aberrant, and missing values. In addition, by analyzing the correlation between the data, the possible periods for forecasting electricity consumption were determined. The experimental results carried out on the Individual Household Electricity Power Consumption dataset showed a clear superiority of the proposed model over most of the ST and/or AI-based models proposed in the literature.

In Sub-Saharan Africa, zoonotic diseases are the leading cause of sickness and mortality, yet preventing their spread has long been difficult. Vaccination initiatives have significantly reduced the frequency of zoonotic diseases mostly in African regions. Nonetheless, zoonotic illnesses continue to be a hazard to underdeveloped countries. Zoonotic infections are spread by direct contact, food, and water. We construct an epidemic model to understand zoonotic disease transmission phenomena. The model is examined using the fundamental results of fractional theory. The reproduction parameter ℛ 0 {{\mathcal{ {\mathcal R} }}}_{0} was obtained by inspecting the model’s steady states. The stability of the system’s steady states has been demonstrated. The system’s reproduction parameter is quantitatively explored by varying various input parameters. Furthermore, the presence and uniqueness of the solution of the proposed dynamics of zoonotic diseases have been demonstrated. Different simulations of the recommended zoonotic disease model with different input factors are performed to inspect the complex dynamics of zoonotic disease with the influence of various model factors. To establish effective prevention and control measures for the infection, we analyse dynamical behaviour of the system. Decreasing the fractional order θ \theta can decrease the infection level significantly. Different factors for reducing zoonotic diseases were recommended to regional policymakers.

In this article, inspired by the projection technique of Solodov and Svaiter, we exploit the simple structure, low memory requirement, and good convergence properties of the mixed conjugate gradient method of Stanimirović et al. [ New hybrid conjugate gradient and broyden-fletcher-goldfarbshanno conjugate gradient methods , J. Optim. Theory Appl. 178 (2018), no. 3, 860–884] for unconstrained optimization problems to solve convex constrained monotone nonlinear equations. The proposed method does not require Jacobian information. Under monotonicity and Lipschitz continuity assumptions, the global convergence properties of the proposed method are established. Computational experiments indicate that the proposed method is computationally efficient. Furthermore, the proposed method is applied to solve the ℓ 1 {\ell }_{1} -norm regularized problems to decode sparse signals and images in compressive sensing.

This paper presents some variants of minimal point theorem together with corresponding variants of Ekeland variational principle. In the second part of this article, there is a discussion on Ekeland variational principle and minimal point theorem relative to it in uniform spaces. The aim of these series of important results is to highlight relations between them, some improvements and specific applications.

The aim of this paper is to study existence and uniqueness of coupled fixed point for a family of self-mappings satisfying a new coupled implicit relation in a Hilbert space. We also prove well-posedness of a coupled fixed point problem.

The pointwise estimates of the deviation T n , A f ( ⋅ ) − f ( ⋅ ) {T}_{n,A}f(\cdot )-f\left(\cdot ) in terms of pointwise moduli of continuity based on the points of differentiability of indefinite integral of f f , with application of the r th differences of the entries of A A , are proved. The similar results in case of the Lebesgue points are considered, too. Analogical results on norm approximation with remarks and corollaries are also given.

Generalized approximate weak greedy algorithms (gAWGAs) were introduced by Galatenko and Livshits as a generalization of approximate weak greedy algorithms, which, in turn, generalize weak greedy algorithm and thus pure greedy algorithm. We consider a narrower case of gAWGA in which only a sequence of absolute errors { ξ n } n = 1 ∞ {\left\{{\xi }_{n}\right\}}_{n=1}^{\infty } is nonzero. In this case sufficient condition for a convergence of a gAWGA expansion to an expanded element obtained by Galatenko and Livshits can be written as ∑ n = 1 ∞ ξ n 2 < ∞ {\sum }_{n=1}^{\infty }{\xi }_{n}^{2}\lt \infty . In the present article, we relax this condition and show that the convergence is guaranteed for ξ n = o 1 n {\xi }_{n}=o\left(\frac{1}{\sqrt{n}}\right) . This result is sharp because the convergence may fail to hold for ξ n ≍ 1 n {\xi }_{n}\hspace{0.33em}\asymp \hspace{0.33em}\frac{1}{\sqrt{n}} .

This paper deals with weighted Lupaş post-quantum Bernstein blending functions and Bézier curves constructed with the help of bases via ( p , q ) \left(p,q) -integers. These blending functions form normalized totally positive bases. Due to the rational nature of weighted Lupaş post-quantum Bézier curves and positive weights, they help in investigating from geometric point of view. Their degree elevation properties and de Casteljau algorithm have been studied. It has been shown that quadratic weighted Lupaş post-quantum Bézier curves can represent conic sections in two-dimensional plane. Graphical analysis has been presented to discuss geometric interpretation of weight and conic section representation by weighted Lupaş post-quantum Bézier curves. This new generalized weighted Lupaş post-quantum Bézier curve provides better approximation and flexibility to a particular control point as well as control polygon due to extra parameter p p and q q in comparison to classical rational Bézier curves, Lupaş q q -Bézier curves and weighted Lupaş q q -Bézier curves.

For an entire function solution of generalized bi-axisymmetric potential equation, we obtain a relationship between the generalized growth characteristics and polynomial approximation errors in sup norm by using the general functions introduced by Seremeta [ On the connection between the growth of the maximum modulus of an entire function and the moduli of the coefficients of its power series expansion , Amer. Math. Soc. Transl. 88 (1970), no. 2, 291–301].

In this article, fixed point results for self-mappings in the setting of two metrics satisfying F F -lipschitzian conditions of rational-type are proved, where F F is considered as a semi-Wardowski function with constant τ ∈ R \tau \in {\mathbb{R}} instead of τ > 0 \tau \gt 0 . Two metrics have been considered, one as an incomplete while the other is orbitally complete. The mapping is taken to be orbitally continuous from one metric to another. Some examples are provided to validate our results. For applications, we present existence results for the solutions of a new type of ABC-fractional boundary value problem.

Two-dimensional biharmonic boundary-value problems are considered by the linear barycentric rational collocation method, and the unknown function is approximated by the barycentric rational polynomial. With the help of matrix form, the linear equations of the discrete biharmonic equation are changed into a matrix equation. From the convergence rate of barycentric rational polynomial, we present the convergence rate of linear barycentric rational collocation method for biharmonic equation. Finally, several numerical examples are provided to validate the theoretical analysis.

The basic aim of this study is to include nonnegative real parameters to allow for approximation findings of the Stancu variant of Phillips operators. We concentrate on the uniform modulus of smoothness in a simple manner before moving on to the approximation in weighted Korovkin’s space. Our study’s goals and outcomes are to fully develop the uniformly approximated findings of Phillips operators. We determine the order of convergence in terms of Lipschitz maximal function and Peetre’s K-functional. In addition, the Voronovskaja-type theorem is also proved.

In this article, by virtue of expansions of two finite products of finitely many square sums, with the aid of series expansions of composite functions of (hyperbolic) sine and cosine functions with inverse sine and cosine functions, and in the light of properties of partial Bell polynomials, the author establishes Taylor’s series expansions of real powers of two functions containing squares of inverse (hyperbolic) cosine functions in terms of the Stirling numbers of the first kind, presents a closed-form formula of specific partial Bell polynomials at a sequence of derivatives of a function containing the square of inverse cosine function, derives several combinatorial identities involving the Stirling numbers of the first kind, demonstrates several series representations of the circular constant Pi and its real powers, recovers Maclaurin’s series expansions of positive integer powers of inverse (hyperbolic) sine functions in terms of the Stirling numbers of the first kind, and also deduces other useful, meaningful, and significant conclusions and an application to the Riemann zeta function.

By using the theory of fixed point index and spectral theory of linear operators, we study the existence of positive solutions for Riemann-Liouville fractional differential equations at resonance. Our approach will provide some new ideas for the study of this kind of problem.

This article establishes an asymptotic behavior for the elasticity systems with nonlinear source and dissipative terms in a three-dimensional thin domain, which generalizes some previous works. We consider the limit when the thickness tends to zero, and we prove that the limit solution u ∗ {u}^{\ast } is a solution of a two-dimensional boundary value problem with lower Tresca’s free-boundary conditions. Moreover, we obtain the weak Reynolds-type equation.

The time-fractional cable model is solved using an extended cubic B-spline (ECBS) collocation strategy. The B-spline function was used for space partitioning, while the Caputo-Fabrizio (CF) was used for temporal discretization. The finite difference technique was used to discretize the CF operator. For the first time in cable modeling, the CF operator has been used. In terms of time, the convergence of order τ \tau . An ECBS collocation approach is investigated by numerical example at different values, and comparisons with published work are made. The numerical results show that the scheme performed well, and the graphical representations show that the results are very close to exact values. The Von Neumann technique is applied to investigate the stability of the proposed scheme.

This article is aimed at establishing some results concerning integral inequalities of the Opial type in the fractional calculus scenario. Specifically, a generalized definition of a fractional integral operator is introduced from a new Raina-type special function, and with certain results proposed in previous publications and the choice of the parameters involved, the established results in the work are obtained. In addition, some criteria are established to obtain the aforementioned inequalities based on other integral operators. Finally, a more generalized definition is suggested, with which interesting results can be obtained in the field of fractional integral inequalities.

In this study, we have proposed a mathematical model to describe the dynamics of the spread of Middle East Respiratory Syndrome disease. The model consists of six-coupled ordinary differential equations. The existence of the corona-free equilibrium and endemic equilibrium points has been proved. The threshold condition for which the disease will die out or becomes permanent has been computed. That is the corona-free equilibrium point is locally asymptotically stable whenever the reproduction number is less than unity, and it is globally asymptotically stable (GAS) whenever the reproduction number is greater than unity. Moreover, we have proved that the endemic equilibrium point is GAS whenever the reproduction number is greater than unity. The results of the model analysis have been illustrated by numerical simulations.

This article investigates the problem of rapid exponential stabilization for nonlinear continuous systems via event-triggered impulsive control (ETIC). First, we propose a trigger mechanism that, when triggered by a predefined event, causes the closed-loop system exponentially stable. Then, the exponential stabilization is achieved by the designed ETIC with or without data dropout. The case where there are delays in the ETIC signals is also studied, and the exponential stabilization is proved. Finally, a numerical study is presented, along with numerical illustrations of the stability results.

In this article, we obtained new infinite sets of exact soliton solutions for the nonlinear evolution system of three-wave resonant interaction equations. The solved system contains the non-zero second-order dispersion coefficients, the non-zero phase velocity mismatch, and the conformable fractional time derivative of order between zero and one. The solution method is a constructed ansatz that consists of linear combinations of the tan and cotan hyperbolic functions with complex coefficients. We stated clear systematic steps toward writing an exact soliton solution for the studied system. To show the efficiency of this method, we introduced some numerical examples on each obtained set of solutions. The computations showed that similar solutions can be obtained if one replaces the tan and cotan hyperbolic functions with the tan and cotan trigonometric functions. The new obtained fractional solutions could be useful in studying the broad applications of triad resonances in plasma physics and in nonlinear optics.

COVID-19, a novel coronavirus disease, is still causing concern all over the world. Recently, researchers have been concentrating their efforts on understanding the complex dynamics of this widespread illness. Mathematics plays a big role in understanding the mechanism of the spread of this disease by modeling it and trying to find approximate solutions. In this study, we implement a new technique for an approximation of the analytic series solution called the multistep Laplace optimized decomposition method for solving fractional nonlinear systems of ordinary differential equations. The proposed method is a combination of the multistep method, the Laplace transform, and the optimized decomposition method. To show the ability and effectiveness of this method, we chose the COVID-19 model to apply the proposed technique to it. To develop the model, the Caputo-type fractional-order derivative is employed. The suggested algorithm efficacy is assessed using the fourth-order Runge-Kutta method, and when compared to it, the results show that the proposed approach has a high level of accuracy. Several representative graphs are displayed and analyzed in two dimensions to show the growth and decay in the model concerning the fractional parameter α values. The central processing unit computational time cost in finding graphical results is utilized and tabulated. From a numerical viewpoint, the archived simulations and results justify that the proposed iterative algorithm is a straightforward and appropriate tool with computational efficiency for several coronavirus disease differential model solutions.

A short account of some recent existence, multiplicity, and uniqueness results for singular p -Laplacian problems either in bounded domains or in the whole space is performed, with a special attention to the case of convective reactions. An extensive bibliography is also provided.

In this article, we will prove the existence of infinitely many solutions for a class of quasilinear Schrödinger equations without assuming the 4-superlinear at infinity on the nonlinearity. We achieve our goal by using the Fountain theorem.

In this work, we are interested at the existence of nontrivial solutions for a nonlinear elliptic problem with resonance part and nonlinear boundary conditions. Our approach is variational and is based on the well-known Landesman-Laser-type conditions.

The aim of this paper is to study the existence and the asymptotic stability of solutions for an epidemiologically emerging reaction-diffusion model. We show that the model has two types of equilibrium points to resolve the proposed system for a fairly broad class of nonlinearity that describes the transmission of an infectious disease between individuals. The model is analyzed by using the basic reproductive number R 0 {R}_{0} . Finally, we present the numerical examples simulations that clarifies and confirms the results of the study throughout the paper.

The aim of this article is to study the fully degenerate Bernoulli polynomials and numbers, which are a degenerate version of Bernoulli polynomials and numbers and arise naturally from the Volkenborn integral of the degenerate exponential functions on Z p {{\mathbb{Z}}}_{p} . We find some explicit expressions for the fully degenerate Bernoulli polynomials and numbers in terms of the degenerate Stirling numbers of the second kind, the degenerate r r -Stirling numbers of the second kind, and the degenerate Stirling polynomials. We also consider the degenerate poly-Bernoulli polynomials and derive explicit representations for them in terms of the same degenerate Stirling numbers and polynomials.

Wigner-Ville transform or Wigner-Ville distribution (WVD) associated with quaternion offset linear canonical transform (QOLCT) was proposed by Bhat and Dar. This work is devoted to the development of the theory proposed by them, which is an emerging tool in the scenario of signal processing. The main contribution of this work is to introduce WVD and ambiguity function (AF) associated with the QOLCT (WVD-QOLCT/AF-QOLCT). First, the definition of the WVD-QOLCT is proposed, and then several important properties such as dilation, nonlinearity, and boundedness are derived. Second, we derived the AF for the proposed transform. A bunch of important properties, including the reconstruction formula associated with the AF, are studied.

The degenerate Stirling numbers of the second kind were introduced as a degenerate version of the ordinary Stirling numbers of the second kind. They appear very frequently when one studies various degenerate versions of some special numbers and polynomials. The aim of this article is to further study some identities and properties related to the degenerate Stirling numbers of the second kind, in connection with the degenerate Bell polynomials, the degenerate Fubini polynomials, the degenerate Bernoulli polynomials, and the degenerate Euler polynomials.

In this article, the authors present two identities involving products of the Bernoulli numbers, provide four alternative proofs for these two identities, derive two closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of the second kind, and supply simple proofs of series expansions of (hyperbolic) cosecant and cotangent functions.

Recently, Kim-Kim [J. Math. Anal. Appl. 493 (2021), no. 1] introduced the degenerate Sheffer sequence and λ -Sheffer sequence. The purpose of this article is to study λ - q -Sheffer sequence and the degenerate q -Sheffer sequence, which are derived from the view point of degenerate umbral calculus and investigate some properties related to those sequences. In addition, we give some new identities associated with q -special polynomials arising from our investigation.

This work is concerned with a multi-dimensional viscoelastic pseudo-parabolic equation with critical Sobolev exponent. First, with some suitable conditions, we prove that the weak solution exists globally. Next, we show that the stability of the system holds for a much larger class of kernels than the ones considered in previous literature. More precisely, we consider the kernel g : [ 0 , ∞ ) ⟶ ( 0 , ∞ ) g:{[}0,\infty )\hspace{0.33em}\longrightarrow \hspace{0.33em}(0,\infty ) satisfying g ′ ( t ) ⩽ − ξ ( t ) G ( g ( t ) ) {g}^{^{\prime} }(t)\leqslant -\xi (t)G(g(t)) , where ξ \xi and G G are functions satisfying some specific properties.

In this article, we prove a common fixed point theorem for commutative nonlinear mappings that jointly satisfy a certain condition. From the main theorem, a common fixed point theorem for commutative generalized hybrid mappings is derived as a special case. Our novel approach significantly expands the applicable range of mappings for well-known fixed point theorems to be effective. Examples are presented to explicitly illustrate this contribution.

The motive of this article is to study a modified iteration scheme for monotone nonexpansive mappings in the class of uniformly convex Banach space and establish some convergence results. We obtain weak and strong convergence results. In addition, we present a nontrivial numerical example to show the convergence of our iteration scheme. To demonstrate the utility of our scheme, we discuss the solution of nonlinear integral equations as an application, which is again supported by a nontrivial example.

Involving w w -distances we prove a fixed point theorem of Caristi-type in the realm of (non-necessarily T 1 {T}_{1} ) quasi-metric spaces. With the help of this result, a characterization of quasi-metric completeness is obtained. Our approach allows us to retrieve several key examples occurring in various fields of mathematics and computer science and that are modeled as non- T 1 {T}_{1} quasi-metric spaces. As an application, we deduce a characterization of complete G G -metric spaces in terms of a weak version of Caristi’s theorem that involves a G -metric version of w -distances.

In this article, we are interested in the linear conformable diffusion equation on the sphere. Our main goal is to establish some results on the continuity problem with respect to fractional order. The main technique is based on several evaluations on the sphere using spherical basis functions. To overcome the difficulty, we also need to use some calculations to control the generalized integrals.