Convergence Analysis of Some Faster Iterative Schemes for $G$-Nonexpansive Mappings in Convex Metric Spaces Endowed with a Graph

Godwin Amechi Okeke, Mujahid Abbas

Abstract

We propose two iterative schemes for three $G$-nonexpansive mappings and present their convergence analysis in the framework of a convex metric space endowed with a directed graph. Some numerical examples are given to support the claim that the proposed iterative schemes converge faster than all of Mann, Ishikawa and Noor iteration schemes. Our results generalize and extend several known results to the setup of a convex metric space endowed with a directed graphic structure, including the results in [S. Suantai, M. Donganont, W. Cholamjiak, Hybrid methods for a countable family of $G$-nonexpansive mappings in Hilbert spaces endowed with graphs, Mathematics (2019)].