PPF-Dependent Fixed Point Results for New Multi-Valued Generalized F-Contraction in the Razumikhin Class with an Application

In this paper, a new multi-valued generalized F-contraction mapping is given. Using it, the existence of PPF-dependent fixed point for such mappings in the Razumikhin class is obtained. Moreover, an application for nonlinear integral equations with delay is presented here to illustrate the usability of the obtained results

FIXED POINT RESULTS IN COMPLEX VALUED METRIC SPACES WITH AN APPLICATION

In this paper, we introduce fixed point theorem for a general contractive condition in complex valued metric spaces. Also, some important corollaries under this contractive condition areobtained. As an application, we find a unique solution for Urysohn integral equations and some illustrative examples are given to support our obtaining results. Our results extend and generalize the results of Azam et al. [2] and some other known results in the literature

Exciting Fixed Point Results under a New Control Function with Supportive Application in Fuzzy Cone Metric Spaces

The objective of this paper is to present a new notion of a tripled fixed point (TFP) findings by virtue of a control function in the framework of fuzzy cone metric spaces (FCM-spaces). This function is a continuous one-to-one self-map that is subsequentially convergent (SC) in FCM-spaces. Moreover, by using the triangular property of a FCM, some unique TFP results are shown under modified contractive-type conditions. Additionally, two examples are discussed to uplift our work. Ultimately, to examine and support the theoretical results, the existence and uniqueness solution to a system of Volterra integral equations (VIEs) are obtained.This work was supported in part by the Basque Government under Grant IT1207-19

Application to Lipschitzian and Integral Systems via a Quadruple Coincidence Point in Fuzzy Metric Spaces

In this paper, the results of a quadruple coincidence point (QCP) are established for commuting mapping in the setting of fuzzy metric spaces (FMSs) without using a partially ordered set. In addition, several related results are presented in order to generalize some of the prior findings in this area. Finally, to support and enhance our theoretical ideas, non-trivial examples and applications for finding a unique solution for Lipschitzian and integral quadruple systems are discussed.This work was supported in part by the Basque Government under Grant IT1207-19

A Weak Tripled Contraction for Solving a Fuzzy Global Optimization Problem in Fuzzy Metric Spaces

In the setting of fuzzy metric spaces (FMSs), a global optimization problem (GOP) obtaining the distance between two subsets of an FMS is solved by a tripled fixed-point (FP) technique here. Also, fuzzy weak tripled contractions (WTCs) for that are given. This problem was known before in metric space (MS) as a proximity point problem (PPP). The result is correct for each continuous τ —norms related to the FMS. Furthermore, a non-trivial example to illustrate the main theorem is discussed.This work was supported in part by the Basque Government under Grant IT1207-19

A COMMON RANDOM FIXED POINT THEOREM OF RATIONAL INEQUALITY IN POLISH SPACES WITH APPLICATION

In this paper, we prove a new common random fixed point theorem for a pair of random operators satisfying random F-contraction of rational inequality in polish spaces. An application to a system of random nonlinear integral equations is discussed. Finally, we give some examples to verify our results

Advanced Algorithms and Common Solutions to Variational Inequalities

The paper aims to present advanced algorithms arising out of adding the inertial technical and shrinking projection terms to ordinary parallel and cyclic hybrid inertial sub-gradient extra-gradient algorithms (for short, PCHISE). Via these algorithms, common solutions of variational inequality problems (CSVIP) and strong convergence results are obtained in Hilbert spaces. The structure of this problem is to find a solution to a system of unrelated VI fronting for set-valued mappings. To clarify the acceleration, effectiveness, and performance of our parallel and cyclic algorithms, numerical contributions have been incorporated. In this direction, our results unify and generalize some related papers in the literature.This work was supported in part by the Basque Government under Grant IT1207-19

A New Four-Step Iterative Procedure for Approximating Fixed Points with Application to 2D Volterra Integral Equations

This work is devoted to presenting a new four-step iterative scheme for approximating fixed points under almost contraction mappings and Reich–Suzuki-type nonexpansive mappings (RSTN mappings, for short). Additionally, we demonstrate that for almost contraction mappings, the proposed algorithm converges faster than a variety of other current iterative schemes. Furthermore, the new iterative scheme’s ω2—stability result is established and a corroborating example is given to clarify the concept of ω2—stability. Moreover, weak as well as a number of strong convergence results are demonstrated for our new iterative approach for fixed points of RSTN mappings. Further, to demonstrate the effectiveness of our new iterative strategy, we also conduct a numerical experiment. Our major finding is applied to demonstrate that the two-dimensional (2D) Volterra integral equation has a solution. Additionally, a comprehensive example for validating the outcome of our application is provided. Our results expand and generalize a number of relevant results in the literature.This work was supported in part by the Basque Government under Grant IT1555-22

Existence and stability results for a coupled system of impulsive fractional differential equations with Hadamard fractional derivatives

The purpose of this study is to give some findings on the existence, uniqueness, and Hyers-Ulam stability of the solution of an implicit coupled system of impulsive fractional differential equations possessing a fractional derivative of the Hadamard type. The existence and uniqueness findings are obtained using a fixed point theorem of the type of Kransnoselskii. In keeping with this, many forms of Hyers-Ulam stability are examined. Ultimately, to support main results, an example is provided.This work was supported in part by the Basque Government under Grant IT1555-22

Fixed point approach to the Mittag-Leffler kernel-related fractional differential equations

The goal of this paper is to present a new class of contraction mappings, so-called -contractions. Also, in the context of partially ordered metric spaces, some coupled fixed-point results for -contraction mappings are introduced. Furthermore, to support our results, two examples are provided. Finally, the theoretical results are applied to obtain the existence of solutions to coupled fractional differential equations with a Mittag-Leffler kernel.This work was supported in part by the Basque Government under Grant IT1555-22