Abstract: In this paper, we introduce an explicit iterative scheme for approximating common fixed points for a finite family of $G$-nonexpansive mappings in a uniformly convex Banach space with a directed graph. Our results extend and improve the results of [Tripak, O.: Common fixed points of $G$-nonexpansive mappings on Banach spaces with a graph, Fixed Point Theory Appl. doi:10.1186/s13663-016-0578-4 (2016)] and other results in the literature.
Key words: Mann and Ishikawa iteration scheme, three-step Noor-iteration scheme, Weak and strong convergence, common fixed points, $G$-nonexpansive mappings, digraph.
How to cite this article:
Tibebu Worku Hunde, Mengistu Goa Sangago and Habtu Zegeye, Approximation of a Common Fixed Point of a Family of $G$-Nonexpansive Mappings in Banach Spaces with a Graph, International Journal of Advances in Mathematics, Volume 2017, Number 6, Pages 137-152, 2017.