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The main goal of this study was to look into some new integral transformations that are associated with a generalized kk-Bessel function. Integral formulas for the generalized kk-Bessel function have been established using the Laplace transform, Euler transform, Whittaker transform, and kk-transforms. The results presented here have the potential to be helpful, and some special cases of corollaries are explicitly demonstrated.

We consider the class of functions u ∈ C²((0, ∞)) satisfying second-order differential inequalities in the form u'(x) + k/x²u(x) ≥ 0 for all x > 0. For this class of functions, we establish Hermite-Hadamard-type inequalities in both cases (k = 1/4 and 0 < k < 1/4 ). We next extend our obtained results to the two-dimensional case. In the limit case k → 0+ we deriver some existing results from the literature that are related to convex functions and convex functions on the coordinates. In our approach, we make use of some tools from ordinary differential equations. [ABSTRACT FROM AUTHOR]

In the present paper, we study the existence and convergence of the best proximity point for cyclic Θ\Theta -contractions. As consequences, we extract several fixed point results for such cyclic mappings. As an application, we present some solvability theorems in the topic of variational inequalities.

This work primarily delves into three key areas: the presence of mild solutions, exploration of the topological and geometrical makeup of solution sets, and the continuous dependency of solutions on a second-order semilinear integro-differential inclusion. The Bohnenblust-Karlin fixedpoint method has been integrated with Grimmer's theory of resolvent operators. Ultimately, the study delves into a mild solution for a partial integro-differential inclusion to showcase the achieved outcomes. [ABSTRACT FROM AUTHOR]

We introduce the class of ψ-convex functions f: [0, ∞) → R, where ψ ∈ C([0, 1]) satisfies ψ ≥ 0 and ψ(0) ̠ ψ(1). This class includes several types of convex functions introduced in previous works. We first study some properties of such functions. Next, we establish a double Hermite-Hadamard-type inequality involving ψ-convex functions and a Simpson-type inequality for functions f ∈ C¹([0, ∞)) such that |f'| is ψ-convex. Our obtained results are new and recover several existing results from the literature. [ABSTRACT FROM AUTHOR]

In this study, we demonstrate that fixed points can occur in extended b-metric spaces that are not necessarily complete. We must employ a novel form of contraction conditions in order to relax the completeness criterion. It has been investigated how fixed points behave in both partially complete and orbitally complete spaces. We provide some instances to highlight our findings. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to find some fixed point results with a new approach, particularly in those cases where the existing literature remains silent. More precisely, we introduce partial completeness, f̄-orbitally completeness, a new type of contractions and many other notions. We also ensure the existence of fixed points for non-contraction maps in the class of incomplete partial b-metric spaces. We have reported some examples in support of our results.

In this work, we show that the existence of fixed points of F-contraction mappings in function weighted metric spaces can be ensured without third condition (F3)(F3) imposed on Wardowski function F:(0, ∞)→ℜF\mathrm{:(0,\hspace{0.33em}}\infty )\to \Re . The present article investigates (common) fixed points of rational type F-contractions for single-valued mappings. The article employs Jleli and Samet’s perspective of a new generalization of a metric space, known as a function weighted metric space. The article imposes the contractive condition locally on the closed ball, as well as, globally on the whole space. The study provides two examples in support of the results. The presented theorems reveal some important corollaries. Moreover, the findings further show the usefulness of fixed point theorems in dynamic programming, which is widely used in optimization and computer programming. Thus, the present study extends and generalizes related previous results in the literature in an empirical perspective.

In this study, we work with the relative divergence of type s,s∈ℝs,s\in {\mathbb{R}}, which includes the Kullback-Leibler divergence and the Hellinger and χ 2 distances as particular cases. We study the symmetrized divergences in additive and multiplicative forms. Some basic properties such as symmetry, monotonicity and log-convexity are established. An important result from the convexity theory is also proved.

In this study, we develop the concept of multivalued Suzuki-type θ-contractions via a gauge function and established two new related fixed point theorems on metric spaces. We also discuss an example to validate our results.

In this paper, we introduce a rough quotient. Also, we present conditions ensuring that G/H are partitions of G. The rough projection map is also presented. We discuss first, second and third rough isomorphism theorems and other related results. At the end, an orbit and a stabilizer in topological rough groups are considered.