Volume 44, Issue 4

In the current investigation, we offer the generalized version of q 1 ⁢ q 2 {q_{1}q_{2}} -Simpson’s type inequalities via ( α , m ) {(\alpha,m)} -coordinated convex functions. To validate their generalized behavior, we demonstrate the link between our outcomes and the already derived ones. Moreover, we provide some application to special means of positive real numbers to support our findings. The principal outcomes raised in this investigation are extensions and generalizations of the comparable results in the history on Simpson’s inequalities for coordinated convex functions.

This research paper aims to introduce the concept of lacunary ideal Cauchy sequences of fuzzy variables in a credibility space. We establish the interrelationships between this notion with lacunary ideal convergent sequences in the same structure from several aspects of credibility. Furthermore, we explore the concepts of strongly lacunary Cauchy, strongly ℐ {\mathcal{I}} -lacunary Cauchy, and strongly ℐ ∗ {\mathcal{I}^{\ast}} -lacunary Cauchy sequences of fuzzy variables within the context of credibility. We also examine the interconnections between these concepts and analyze their relationships.

The aim of this paper is to prove a generalization of Titchmarsh’s theorems for the generalized Fourier transform called ( κ , n {\kappa,n} )-Fourier transform, where n is a positive integer and κ is a constant coming from Dunkl theory. As an application, we derive a ( κ , n ) {(\kappa,n)} -Fourier multiplier theorem for L 2 {L^{2}} Lipschitz spaces. Moreover, we give necessary conditions to ensure that f belongs to either one of the generalized Lipschitz classes of order m . This allows us to establish the analogue of the Boas-type result for ℱ κ , n {\mathcal{F}_{\kappa,n}} .

In this paper, our main interest is to propose a viscosity iterative method for approximating solutions of variational inequality problems, resolvents of monotone operators and fixed points of ρ-demimetric mappings with multiple output sets in Hadamard spaces. We prove a strong convergence result for approximating the solutions of the aforementioned problems under some mild conditions. Also, we present an application of our main result to a convex minimization problem. Our results improve and generalize many related results in the literature.

In this paper, we express a generalization of the Ramanujan integral I ⁢ ( α ) {I(\alpha)} with the analytical solutions, using the Laplace transform technique and some algebraic relation or the Pochhammer symbol. Moreover, we evaluate some consequences of a generalized definite integral ϕ * ⁢ ( υ , β , a ) {\phi^{*}(\upsilon,\beta,a)} . The well-known special cases appeared, whose solutions are possible by Cauchy’s residue theorem, and many known applications of the integral I ⁢ ( a , β , υ ) {I(a,\beta,\upsilon)} are discussed by the Leibniz rule for differentiation under the sign of integration. Further, one closed-form evaluation of the infinite series of the F 0 1 ⁢ ( ⋅ ) {{}_{1}F_{0}(\,\cdot\,)} function is deduced. In addition, we establish some integral expressions in terms of the Euler numbers, which are not available in the tables of the book of Gradshteyn and Ryzhik.

In this paper, we define and study three novel summability concepts – strong deferred 𝜎-summability, deferred 𝜎-statistical summability, and 𝜎-statistical summability in intuitionistic fuzzy 𝑟-normed linear spaces (briefly called IF-𝑟-NLS) by using 𝜎-mean. We also provide an example in support of the new notions and uncover some interesting relationships. Additionally, we study deferred 𝜎-statistical summability in the context of two pairs of sequences of positive integers, namely, α n , γ n \alpha_{n},\gamma_{n} , and u n , v n u_{n},v_{n} satisfying α n ≤ u n < v n ≤ γ n \alpha_{n}\leq u_{n}<v_{n}\leq\gamma_{n} .

The aim of this article is to present, in a specific metric space, a density theorem. Then, as an application, we give a relaxation theorem for a first-order set-differential inclusion, through an abstract convexity notion.

The main purpose of this paper is to study η-Ricci–Yamabe solitons (η-RYS) and * {*} -η-Ricci–Yamabe solitons ( * {*} -η-RYS) in Lorentzian para-Kenmotsu n -manifolds (briefly, ( LPK ) n {(\mathrm{LPK})_{n}} ). We study the curvature condition R . S = 0 {R.S=0} and the cyclic parallel Ricci tensor in ( LPK ) n {(\mathrm{LPK})_{n}} admitting η-RYS. Furthermore, we study M -projectively flat and quasi- M -projectively flat Lorentzian para-Kenmotsu manifolds admitting * {*} -η-RYS. Finally, we give two examples of Lorentzian para-Kenmotsu manifolds admitting η-RYS and * {*} -η-RYS to verify some of our results.