Fixed Point Theorems for Noncyclic Monotone Relativelyρ-Nonexpansive Mappings in Modular Spaces

Abstract

In this paper, we obtain some fixed point results for noncyclic monotone ρ-nonexpansive mappings in uniformly convex modular spaces and uniformly convex in every direction modular spaces. As an application, we prove the existence of the solution of an integral equation.

On best proximity point theorems for relatively nonexpansive mappings in locally convex spaces

“…An influential best proximity point theorem, attributed to Fan [7], asserts that within a Hausdorff locally convex topological vector space H, if K represents a compact and convex nonempty subset, and T stands as a continuous self-mapping over K, then the existence of an element υ within K is guaranteed, satisfying p(υ, Tυ) = p(Tυ, K). This theorem has been extended by several authors, including Chaira et al [1], Chi et al [3], El harmouchi et al [5], Espìnola [6], Prolla [9], Reich [11], Saadaoui et al [12] and Sehgal and Singh [13,14], across a variety of frameworks.…”