### Demiclodeness and fixed points of g-asymptotically nonexpansive mapping in Banach spaces with graph

#### Abstract

Let C be a nonempty closed convex subset of a uniformly convex Banach space endowed with a transitive directed graph G = (V(G), E(G)), such that V(G) =C and E(G) is convex. We introduce the definition of G-asymptotically nonexpansive self-mapping on C. It is shown that such mappings are G-demiclosed. Finally, we prove the weak and strong convergence of a sequence generated by a modified Noor iterative process to a common fixed point of a finite family of G-asymptotically nonexpansive self-mappings defined on C with nonempty common fixed points set. Our results improve and generalize several recent results in the literature.

**How to Cite this Article:**Mengistu Goa Sangago, Tibebu Worrku Hunde, Habtu Zegeye Hailu, Demiclodeness and fixed points of g-asymptotically nonexpansive mapping in Banach spaces with graph, Adv. Fixed Point Theory, 8 (2018), 313-340 Copyright © 2018 Mengistu Goa Sangago, Tibebu Worrku Hunde, Habtu Zegeye Hailu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advances in Fixed Point Theory

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