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It has been shown that the findings of d -metric spaces may be deduced from S -metric spaces by considering d ϖ , ϰ = Λ ϖ , ϖ , ϰ . In this study, no such concepts that translate to the outcomes of metric spaces are considered. We establish standard fixed point theorems for integral type contractions involving rational terms in the context of complete S -metric spaces and discuss their implications. We also provide examples to illustrate the work. This paper's findings generalize and expand a number of previously published conclusions. In addition, the abstract conclusions are supported by an application of the Riemann-Liouville calculus to a fractional integral problem and a supportive numerical example. [ABSTRACT FROM AUTHOR]

We introduce the concept of controlled extended Branciari quasi-b-metric spaces, as well as a G q -implicit type mapping. Under this new space setting, we derive some new fixed points, periodic points, right and left Ulam–Hyers stability, right and left weak well-posed properties, and right and left weak limit shadowing results. Additionally, we use these findings to solve the fractional differential equations of a Riesz–Caputo type with integral anti-periodic boundary values, as well of nonlinear matrix equations. All ideas, results, and applications are properly illustrated with examples. [ABSTRACT FROM AUTHOR]

This paper studies existence of solutions for a new class of fractional differential inclusions of arbitrary order with three-point fractional integral boundary conditions. Our results are based on Bohnenblust-Karlin's fixed point theorem. [ABSTRACT FROM AUTHOR]

We present sufficient conditions for the existence of solutions of Fredholm integral inclusion equations using new sort of contractions, named as multivalued almost F -contractions and multivalued almost F -contraction pairs under ı-distance, defined in b-metric spaces. We give its relevance to fixed point results in orbitally complete b-metric spaces. To rationalize the notions and outcome, we illustrate the appropriate examples.

The purpose of this paper is to study common fixed points in complex valued metric spaces and obtain sufficient conditions for the existence of common fixed points of a pair of mappings satisfying generalized contraction involving rational expressions.

The aim of our paper is to use common limit range property for two pairs of mappings deriving common fixed point results under a generalized altering distance function. Some examples are given to exhibit different type of situation which shows the requirements of conditions of our results. At the end the existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming with the help of a common fixed point theorem is presented.

In this study, we consider a non-linear matrix equation of the form X = Q + Σi=1m Σj=1t Ai Fj (X) Ai where Q is a Hermitian positive definite matrix, Ai* stands for the conjugate transpose of an n × n matrix Ai and Fj are order-preserving continuous mappings from the set of all Hermitian matrices to the set of all positive definite matrices such that F(O)=O. We discuss sufficient conditions that ensure the existence of a unique positive definite solution of the given matrix equation. For this, we derive some fixed point results for Suzuki-implicit type mappings on metric spaces (not necessarily complete) endowed with arbitrary binary relation (not necessarily a partial order). We provide adequate examples to validate the fixed-point results and the importance of related work, and the convergence analysis of non-linear matrix equations. [ABSTRACT FROM AUTHOR]

In this paper, we study generalized FG-contraction conditions for a pair of mappings deĄned on a family of subsets of a metric space endowed with a directed graph, and discuss coincidence and common Ąxed point results relaxing the continuity of mappings. The given notions and results are exempliĄed by suitable models. We apply our results to the problem of existence of solutions of a Fredholm integral inclusion. [ABSTRACT FROM AUTHOR]