DOI: 10.24193/fpt-ro.2021.2.37

Authors: Lili Chen, Ni Yang and Yanfeng Zhao

Abstract: The aim of this paper is to introduce Mann iterative algorithm by using the convex structure in the metric space endowed with a directed graph. First of all, the concept of the convex metric space endowed with a directed graph is given. Moreover, Mann iteration scheme and the corresponding convergence theorems for the G-monotone contractive mappings and the G-monotone nonexpansive mappings in convex metric spaces endowed with a directed graph are established respectively. In addition, an example is shown to illustrate that the Mann iterative sequence does not necessarily converge to the fixed point of the G-monotone nonexpansive mapping.

Key Words and Phrases: Metric space endowed with a directed graph, convex structure, Mann iterative algorithm.

2010 Mathematics Subject Classification: 46B20, 46E30, 47H09, 47H10.

Published on-line: July 1st, 2021.

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