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A fixed point theorem for monotone asymptotically nonexpansive mappings

Authors: Monther Rashed Alfuraidan and Mohamed Amine Khamsi
Journal: Proc. Amer. Math. Soc. 146 (2018), 2451-2456
MSC (2010): Primary 46B20, 45D05; Secondary 47E10, 34A12
Published electronically: February 28, 2018
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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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Additional Information

Monther Rashed Alfuraidan
Affiliation: Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Mohamed Amine Khamsi
Affiliation: Department of Mathematical Sciences, University of Texas at El Paso, El Paso, Texas 79968

Keywords: Asymptotic nonexpansive mapping, fixed point, monotone mapping, partially ordered, uniformly convex
Received by editor(s): June 20, 2016
Received by editor(s) in revised form: July 15, 2016
Published electronically: February 28, 2018
Communicated by: Mourad Ismail
Article copyright: © Copyright 2018 American Mathematical Society

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