Strong Convergence of a New Hybrid Iteration for Three Asymptotically Quasi $\mathcal{G}$-$\phi$-Nonexpansive Mappings in Banach Spaces with Directed Graphs

Asian Conference on Fixed Point Theory and Optimization 2023

Abstract

The purpose of the paper is to combine the shrinking projection method with $SP$-iteration to introduce a new hybrid iterative scheme for approximating common fixed points of three asymptotically quasi $\mathcal{G}$-$\phi$-nonexpansive mappings. A strong convergence result for the proposed iteration processes is proved under some suitable conditions in uniformly smooth and uniformly convex Banach spaces with directed graphs without any requirement of the semicompact property of such mappings. Finally, we apply our proposed method to find a solution of the system of the nonlinear integral equations.