Volume 71, Issue 1

The present paper introduces and studies the concepts of K -outer approximation and K -inner approximation for a monotone function μ defined on a D -poset P , by a subfamily K of P . Some desirable properties of K -approximable functions are established and it is shown that the family of all elements of P that possess K -approximation, forms a lattice and is closed under orthosupplementation. We have proved that a submodular measure on a suitable subfamily of P having K -outer approximation can be extended to a function that has K -outer approximation, and a tight function that has K -inner approximation can be extended to a function having K -inner approximation.

In this paper, it is shown that there is no positive integer n such that the set of x∈A$ x\in \mathfrak{A} $ for which [(xδ)n,(x∗δ)n(xδ)n]∈Z(A)$ [(x^{\delta})^n, (x^{*{\delta}})^n(x^{\delta})^n]\in \mathcal{Z}(\mathfrak{A}) $, where δ is a linear derivation on A$ \mathfrak{A} $ or there exists a central idempotent e∈Q$ e\in \mathcal{Q} $ such that δ =0 on eQ$ e\mathcal{Q} $ and (1−e)Q$ (1-e)\mathcal{Q} $ satisfies S 4 ( X 1 , X 2 , X 3 , X 4 ). Moreover, we establish other related results.

The aim of this study is to establish new discrete Grüss type inequality using fractional order h-sum and h-difference operators that generalize the fractional sum and difference operators.

In this manuscript, we introduce and study the concept of exponential trigonometric convex functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for the newly introduced class of functions. We also obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is exponential trigonometric convex function. It has been shown that the result obtained with Hölder-İşcan and improved power-mean integral inequalities give better approximations than that obtained with Hölder and improved power-mean integral inequalities.

In this paper some properties of the pseudo-integral are summarized and a characterization theorem for this integral is proposed. Using the characterization theorem, we obtain that the pseudo-integral with respect to the pseudo-product of two σ -⊕-measures can be reduced to repeated pseudo-integrals. As a consequence of that claim and the Hölder type inequality for the pseudo-integral, we get the generalized Minkowski inequality for the pseudo-integral.

This paper aims to introduce the q -analogue of subclasses of the spiral-like functions of complex order and derive some inclusion properties by applying certain linear operators. The invariance of these classes under q -Bernardi integral operator has been discussed. Our results yield some known results as special case.

This paper studies analytic functions f defined on the open unit disk of the complex plane for which f / g and (1 + z ) g / z are both functions with positive real part for some analytic function g . We determine radius constants of these functions to belong to classes of strong starlike functions, starlike functions of order α , parabolic starlike functions, as well as to the classes of starlike functions associated with lemniscate of Bernoulli, cardioid, lune, reverse lemniscate, sine function, exponential function and a particular rational function. The results obtained are sharp.

We give some sufficient conditions for the convergence of the sequence of successive approximations to the unique solution of first order Cauchy problem in a Banach space. Our approach is based on a generalized Nagumo condition due to A. Constantin and the properties of the Kuratowski measure of noncompactness.

In this article, by using a new form of multi-quadratic mapping, we define multi- m -Jensen-quadratic mappings and then unify the system of functional equations defining a multi- m -Jensen-quadratic mapping to a single equation. Using a fixed point theorem, we study the generalized Hyers-Ulam stability of multi-quadratic and multi- m -Jensen-quadratic functional equations. As a consequence, we show that every multi- m -Jensen-quadratic functional equation (under some conditions) can be hyperstable.

In this article we obtain sufficient conditions for the oscillation of all solutions of the higher-order delay difference equation Δ m(yn− ∑ j=1kpnjyn− mj)+vnG(yσ (n))− unH(yα (n))=fn,$$\begin{array}{} \displaystyle \Delta^{m}\big(y_n-\sum_{j=1}^k p_n^j y_{n-m_j}\big) + v_nG(y_{\sigma(n)})-u_nH(y_{\alpha(n)})=f_n\,, \end{array}$$ where m is a positive integer and Δ x n = x n +1 − x n . Also we obtain necessary conditions for a particular case of the above equation. We illustrate our results with examples for which it seems no result in the literature can be applied.

Recently Bukovský, Das and Šupina [ Ideal quasi - normal convergence and related notions , Colloq. Math. 146 (2017), 265–281] started the study of sequence selection properties (𝓘, 𝓙- α 1 ) and (𝓘, 𝓙- α 4 ) of C p ( X ) using the double ideals, where 𝓘 and 𝓙 are the proper admissible ideals of ω , which are motivated by Arkhangeľskii local α i -properties [ The frequency spectrum of a topological space and the classification of spaces , Dokl. Akad. Nauk SSSR 13 (1972), 1185–1189]. In this paper, we obtain some characterizations of (𝓘, 𝓙- α 1 ) and (𝓘, 𝓙- α 4 ) properties of C p ( X ) in the terms of covering properties and selection principles. Under certain conditions on ideals 𝓘 and 𝓙, we identify the minimal cardinalities of a space X for which C p ( X ) does not have (𝓘, 𝓙- α 1 ) and (𝓘, 𝓙- α 4 ) properties.

In this article we introduce paranormed Nörlund difference sequence space of fractional order α , N t ( p , Δ ( α ) ) defined by the composition of fractional difference operator Δ ( α ) , defined by (Δ (α )x)k=∑ i=0∞ (− 1)iΓ (α +1)i!Γ (α − i+1)xk− i,$\begin{array}{} \displaystyle (\Delta^{(\alpha)}x)_k=\sum_{i=0}^{\infty}(-1)^i\frac{\Gamma(\alpha+1)}{i!\Gamma(\alpha-i+1)}x_{k-i}, \end{array}$ and Nörlund matrix N t . We give some topological properties, obtain the Schauder basis and determine the α −, β − and γ -duals of the new space. We characterize certain matrix classes related to this new space. Finally we investigate certain geometric properties of the space N t ( p , Δ ( α ) ).

Using the theory of elliptic curve, we show that all right triangles, such that the sum of the area and the square of the sum of legs is a square, are given by an infinite set. Similarly, we get all right triangles such that the sum of the area and the square of the semi-perimeter is a square. Using the theory of Pell’s equation, we prove that there are infinitely many non-primitive right triangles such that the sum of the area and the hypotenuse (or the smaller leg) is a square, and an infinity of primitive right triangles such that the sum of the area and the smaller leg (or the perimeter, the semi-perimeter, the larger leg) is a square.

In this paper, we introduce the weighted projective Ricci curvature as an extension of projective Ricci curvature introduced by Z. Shen. We characterize the class of Randers metrics of weighted projective Ricci flat curvature. We find the necessary and sufficient condition under which a Kropina metric has weighted projective Ricci flat curvature. Finally, we show that every projectively flat metric with isotropic weighted projective Ricci and isotropic S-curvature is a Kropina metric or Randers metric.

Let 𝓔 k denote the set of diffeomorphism classes of closed connected smooth k -manifolds X with the property that for any oriented vector bundle α over X , the Euler class e ( α ) = 0. We show that if X ∈ 𝓔 2 n +1 is orientable, then X is a rational homology sphere and π 1 ( X ) is perfect. We also show that 𝓔 8 = ∅ and derive additional cohomlogical restrictions on orientable manifolds in 𝓔 k .

We propose a new generalized class of distributions called Lindley-Weibull Power Series (LWPS) distributions and their special case called Lindley-Weibull logarithmic (LWL) distributions. Structural properties of the LWPS class of distributions and its sub-model LWL distribution including moments, order statistics, Rényi entropy, mean and median deviations, Bonferroni and Lorenz curves, and maximum likelihood estimates are derived. A simulation study to examine the bias and mean square error of the maximum likelihood estimators for each parameter is presented. Finally, real data examples are presented to illustrate the applicability and usefulness of the proposed class of distributions.

In this paper, a stochastic prey-predator model is investigated and analyzed, which possesses foraging arena scheme in polluted environments. Sufficient conditions are established for the extinction and persistence in the mean. These conditions provide a threshold that determines the persistence in the mean and extinction of species. Furthermore, it is also shown that the stochastic system has a periodic solution under appropriate conditions. Finally, several numerical examples are carried on to demonstrate the analytical results.

Let L be a number field. For a given prime p , we define integers αpL$ \alpha_{p}^{L} $ and βpL$ \beta_{p}^{L} $ with some interesting arithmetic properties. For instance, βpL$ \beta_{p}^{L} $ is equal to 1 whenever p does not ramify in L and αpL$ \alpha_{p}^{L} $ is divisible by p whenever p is wildly ramified in L . The aforementioned properties, although interesting, follow easily from definitions; however a more interesting application of these invariants is the fact that they completely characterize the Dedekind zeta function of L . Moreover, if the residue class mod p of αpL$ \alpha_{p}^{L} $ is not zero for all p then such residues determine the genus of the integral trace.