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 | English |
|---|---|
| Article number | 20 |
| Pages (from-to) | 1-9 |
| Number of pages | 9 |
| Journal | Fixed Point Theory and Algorithms for Sciences and Engineering |
| Volume | 2016 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Dec 2016 |
Bibliographical note
Publisher Copyright:© 2016, Bin Dehaish and Khamsi.
Keywords
- Krasnoselskii iteration
- fixed point
- hyperbolic metric spaces
- monotone mapping
- nonexpansive mapping
- partially ordered
- uniformly convex
ASJC Scopus subject areas
- Geometry and Topology
- Applied Mathematics