## A fixed point theorem for monotone asymptotically nonexpansive mappings

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- by Monther Rashed Alfuraidan and Mohamed Amine Khamsi
- Proc. Amer. Math. Soc.
**146**(2018), 2451-2456 - DOI: https://doi.org/10.1090/proc/13385
- 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.## References

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## Bibliographic Information

**Monther Rashed Alfuraidan**- Affiliation: Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
- MR Author ID: 795781
- ORCID: 0000-0002-3641-290X
- Email: monther@kfupm.edu.sa
**Mohamed Amine Khamsi**- Affiliation: Department of Mathematical Sciences, University of Texas at El Paso, El Paso, Texas 79968
- MR Author ID: 100900
- ORCID: 0000-0001-6787-7032
- Email: mohamed@utep.edu
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**146**(2018), 2451-2456 - MSC (2010): Primary 46B20, 45D05; Secondary 47E10, 34A12
- DOI: https://doi.org/10.1090/proc/13385
- MathSciNet review: 3778148