Volume 29, Issue 2

In this paper, we will focus on different types of Świątkowski conditions: Świątkowski, strong Świątkowski and weak Świątkowski conditions. We present the main properties of the families of functions fulfilling such conditions.

We propose an integral transform, called metamorphism, which allows us to reduce the order of a differential equation. For example, the second-order Helmholtz equation is transformed into a first-order equation, which can be solved by the method of characteristics.

In this article, we introduce and study sequence spaces of Cesàro–Nörlund operators of order n associated with a sequence of Orlicz functions. We obtain some topological properties and Schauder basis of these sequence spaces. Moreover, we compute the α-, β- and γ-duals and the matrix transformations of these newly formed sequence spaces. Finally, we prove that these sequence spaces are of Banach–Saks type p and have a weak fixed-point property.

We introduce a large class of contractive mappings, called Suzuki–Berinde type contraction. We show that any Suzuki–Berinde type contraction has a fixed point and characterizes the completeness of the underlying normed space. A fixed point theorem for multivalued mappings is also obtained. These results unify, generalize and complement various known comparable results in the literature.

In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem for the scalar non-viscous diffusive dispersive conservation law where the far field constant state is prescribed. We prove that the solution of the Cauchy problem tends toward the constant state as time goes to infinity.

This paper presents a new trigonometric composite Hermite interpolation method for solving Fredholm linear integral equations. This operator approximates locally both the function and its derivative, which is known on the subdivision nodes. Then we derive a class of quadrature rules with endpoint corrections based on integrating the composite Hermite interpolant. We also provide error estimation and numerical examples to illustrate that this new operator can provide highly accurate results.

In this study, we concentrate on solving the problem of non-Lipschitz absolute value equations (NAVE). A new Bezier curve based smoothing technique is introduced and a new Levenberg–Marquardt type algorithm is developed depending on the smoothing technique. The numerical performance of the algorithm is analysed by considering some well-known and randomly generated test problems. Finally, the comparison with other methods is illustrated to demonstrate the efficiency of the proposed algorithm.

Empirical mode decomposition (EMD) is a popular, user-friendly, data-driven algorithm to decompose a given (non-stationary) signal into its constituting components, utilizing spline interpolation. This algorithm was first proposed in 1998 in the one-dimensional setting, and it employed standard cubic spline interpolation. Since then, different two-dimensional extensions of EMD have been proposed. In this paper, we consider one of these two-dimensional extensions and adapt it to use a shape-preserving interpolation scheme based on quadratic B-splines, ensuring that monotonicity and concavity in the input data are preserved. Using multiple numerical experiments, we show that this new scheme outperforms the original EMD, both qualitatively and quantitatively.

Let X , Y {X,Y} be real, infinite-dimensional Banach spaces. Let ℒ ⁢ ( X , Y ) {{\mathcal{L}}(X,Y)} be the space of bounded operators. An important aspect of understanding differentiability of the operator norm at A ∈ ℒ ⁢ ( X , Y ) {A\in{\mathcal{L}}(X,Y)} is to estimate the limit (which always exists) lim t → 0 + ⁡ ∥ A + t ⁢ B ∥ - ∥ A ∥ t   for  ⁢ B ∈ ℒ ⁢ ( X , Y ) , \lim_{t\rightarrow 0^{+}}\frac{\lVert A+tB\rVert-\lVert A\rVert}{t}\quad\text{% for }B\in{\mathcal{L}}(X,Y), using the values of B on the state space S A = { τ ∈ ℒ ⁢ ( X , Y ) ∗ : τ ⁢ ( A ) = ∥ A ∥ , ∥ τ ∥ = 1 } . S_{A}=\bigl{\{}\tau\in{\mathcal{L}}(X,Y)^{\ast}:\tau(A)=\lVert A\rVert,\,% \lVert\tau\rVert=1\bigr{\}}. In this paper, we give several examples of Banach spaces, including the ℓ p {\ell^{p}} spaces (for 1 < p < ∞ {1<p<\infty} ) where a more tangible estimate is possible, under additional hypotheses on A . We also use the notion of norm-weak upper-semi-continuity (usc, for short) of the preduality map to achieve this. Our results also show that the operator subdifferential limit is related to the corresponding subdifferential limit of the vectors in the range space, when A ∗ ∗ {A^{\ast\ast}} attains its norm.

Over the last few years, numerous researchers have contributed significantly to summability theory by connecting various notions of convergence concepts of sequences. In this paper, we introduce the concepts of ℐ {\mathcal{I}} -statistical supremum and ℐ {\mathcal{I}} -statistical infimum of a real-valued sequence and study some fundamental features of the newly introduced notions. We also introduce the concept of ℐ {\mathcal{I}} -statistical monotonicity and establish the condition under which an ℐ {\mathcal{I}} -statistical monotonic sequence is ℐ {\mathcal{I}} -statistical convergent. We end up giving a necessary and a sufficient condition for the ℐ {\mathcal{I}} -statistical convergence of a real-valued sequence.

In this paper, by considering the identity established by Luo et al. in [C. Luo, T.-S. Du, M. Kunt and Y. Zhang, Certain new bounds considering the weighted Simpson-like type inequality and applications, J. Inequal. Appl. 2018 2018, Paper No. 332] and under the assumption of the quasi-convexity of the first derivative, we establish some new error estimates of the Simpson-like type inequalities. We also discuss the case where the first derivative satisfies the Hölder condition. At the end, we provide some applications to special means. The obtained results represent a continuation of the above-mentioned paper.

In this article, we studied Green’s theorem and the Bochner formula. Further, we apply the Bochner formula to generalized ( k , μ ) {(k,\mu)} -space forms and show that the generalized ( k , μ ) {(k,\mu)} space form is either isometric to a sphere or a certain warped product under some geometric conditions.

The proposed work aims to study the degree of convergence of a function h ~ {\widetilde{h}} , conjugate to a Lebesgue integrable 2 ⁢ π {2\pi} -periodic function h , in the Zygmund class Z r ( ν ) {Z^{(\nu)}_{r}} , r ≥ 1 {r\geq 1} , by almost Nörlund transform. Our results give sharper estimates than the previous existing results.

Convexity is a fundamental concept in analysis. Over the past few decades, many significant error bounds have been established for various quadrature rules using different types of convexity. This paper focuses on the Gauss–Radau quadrature formula. Initially, we introduce a novel identity related to 2-point left Radau-type rule. Next, we derive several integral inequalities for functions whose first derivatives are s -convex in the second sense. Finally, we present applications to special means to demonstrate the effectiveness of our results.

We generalize a size-biased distribution related to the Riemann xi-function using the work of Ferrar. Some analysis and properties of this more general distribution are offered as well.

A class with ambiguous status of its elements by a membership function that assigns to each element a grade in the close interval [ 0 , 1 ] {[0,1]} ; Lofti Zadeh introduced this idea into theory as fuzzy sets in the year of 1965. A study of fuzzy anti-normed linear spaces by Kočinac on some topological properties motivated us to work on fuzzy anti-normed triple sequence spaces with respect to ideal by using compact linear operator. Further, we prove some theorems, particularly on convergence and completeness.

The special matrix functions have received significant attention in many fields, such as theoretical physics, number theory, probability theory, and the theory of group representations. In 2017, Dwivedi and Sahai introduced the generalized hypergeometric matrix function using matrix parameters and proved the convergence on | z | = 1 {|z|=1} . Recently, hypergeometric matrix functions and their potential applications have played a major role in mathematical physics and engineering. Motivated by aforesaid works and in order to enrich this flourishing field, we investigate the Euler-type integral representations for the generalized hypergeometric matrix function and determine various transformations in terms of hypergeometric matrix functions. Furthermore, unit and half arguments have been provided for several particular cases.

Korn’s inequality has been at the heart of much exciting research since its first appearance in the beginning of the 20th century. Many are the applications of this inequality to the analysis and construction of discretizations of a large variety of problems in continuum mechanics. In this paper, we prove that the classical Korn inequality holds true in anisotropic Sobolev spaces. We also prove that an extension of Korn’s inequality, involving non-linear continuous maps, is valid in such spaces. Finally, we point out that another classical inequality, namely Poincaré’s inequality, also holds in anisotropic Sobolev spaces.