Browder and Göhde fixed point theorem for monotone nonexpansive mappings

Buthinah Abdullatif Bin Dehaish; Mohamed Amine Khamsi

doi:10.1186/s13663-016-0505-8

Browder and Göhde fixed point theorem for monotone nonexpansive mappings

Buthinah Abdullatif Bin Dehaish, Mohamed Amine Khamsi

Mathematics

King Abdulaziz University

Research output: Contribution to journal › Article › peer-review

40 Scopus citations

Abstract

Let X be a Banach space or a complete hyperbolic metric space. Let C be a nonempty, bounded, closed, and convex subset of X and (Formula presented.) be a monotone nonexpansive mapping. In this paper, we show that if X is a Banach space which is uniformly convex in every direction or a uniformly convex hyperbolic metric space, then T has a fixed point. This is the analog to Browder and Göhde’s fixed point theorem for monotone nonexpansive mappings.

Original language	British English
Article number	20
Pages (from-to)	1-9
Number of pages	9
Journal	Fixed Point Theory and Applications
Volume	2016
Issue number	1
DOIs	https://doi.org/10.1186/s13663-016-0505-8
State	Published - 1 Dec 2016

Keywords

fixed point
hyperbolic metric spaces
Krasnoselskii iteration
monotone mapping
nonexpansive mapping
partially ordered
uniformly convex

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10.1186/s13663-016-0505-8

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abstract = "Let X be a Banach space or a complete hyperbolic metric space. Let C be a nonempty, bounded, closed, and convex subset of X and (Formula presented.) be a monotone nonexpansive mapping. In this paper, we show that if X is a Banach space which is uniformly convex in every direction or a uniformly convex hyperbolic metric space, then T has a fixed point. This is the analog to Browder and G{\"o}hde{\textquoteright}s fixed point theorem for monotone nonexpansive mappings.",

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N2 - Let X be a Banach space or a complete hyperbolic metric space. Let C be a nonempty, bounded, closed, and convex subset of X and (Formula presented.) be a monotone nonexpansive mapping. In this paper, we show that if X is a Banach space which is uniformly convex in every direction or a uniformly convex hyperbolic metric space, then T has a fixed point. This is the analog to Browder and Göhde’s fixed point theorem for monotone nonexpansive mappings.

AB - Let X be a Banach space or a complete hyperbolic metric space. Let C be a nonempty, bounded, closed, and convex subset of X and (Formula presented.) be a monotone nonexpansive mapping. In this paper, we show that if X is a Banach space which is uniformly convex in every direction or a uniformly convex hyperbolic metric space, then T has a fixed point. This is the analog to Browder and Göhde’s fixed point theorem for monotone nonexpansive mappings.

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KW - hyperbolic metric spaces

KW - Krasnoselskii iteration

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Browder and Göhde fixed point theorem for monotone nonexpansive mappings

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