Browder and Göhde fixed point theorem for monotone nonexpansive mappings

Buthinah Abdullatif Bin Dehaish, Mohamed Amine Khamsi

Research output: Contribution to journalArticlepeer-review

38 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 languageBritish English
Article number20
Pages (from-to)1-9
Number of pages9
JournalFixed Point Theory and Applications
Volume2016
Issue number1
DOIs
StatePublished - 1 Dec 2016

Keywords

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

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