Common fixed points of modified Picard-S iteration process involving two G-nonexpansive mapping in CAT(0) space with directed graph

Sabiya Khatoon, Izhar Uddin, Nuttapol Pakkaranang, Nopparat Wairojjana

Abstract

The aim of this paper is to bring and study the convergence behaviour of modified Picard-S iteration involving two $G$-nonexpansive mappings in CAT(0) space with directed graph. We prove $\Delta$ and strong convergence theorems for modified Picard-S iteration process in CAT(0) space with a directed graph. We also construct a numerical example to validate our results and to ensure the better rate of convergence of the proposed method with modified Ishikawa iteration, modified S-iteration and Thianwan's new iteration.