A fixed point theorem for monotone asymptotically nonexpansive mappings

Alfuraidan, Monther; Khamsi, Mohamed

doi:10.1090/proc/13385

A fixed point theorem for monotone asymptotically nonexpansive mappings
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by Monther Rashed Alfuraidan and Mohamed Amine Khamsi PDF

Proc. Amer. Math. Soc. 146 (2018), 2451-2456 Request permission

Abstract:

Let $C$ be a nonempty, bounded, closed, and convex subset of a Banach space $X$ and $T: C \rightarrow C$ be a monotone asymptotically nonexpansive mapping. In this paper, we investigate the existence of fixed points of $T$. In particular, we establish an analogue to the original Goebel and Kirk’s fixed point theorem for asymptotically nonexpansive mappings.

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