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- Title
MANN ITERATIVE ALGORITHM IN CONVEX METRIC SPACES ENDOWED WITH A DIRECTED GRAPH.
- Authors
LILI CHEN; NI YANG; 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.
- Subjects
METRIC spaces; DIRECTED graphs; NONEXPANSIVE mappings; ALGORITHMS
- Publication
Fixed Point Theory, 2021, Vol 22, Issue 2, p559
- ISSN
1583-5022
- Publication type
Article
- DOI
10.24193/fpt-ro.2021.2.37