Abstract
In this article, we introduce a new approach to common fixed point theory for a weak compatible pair. We first introduce the concepts of R-pair and NR-pair and establish some new common fixed point theorems for a weak compatible pair in hyperconvex metric spaces and uniformly convex metric spaces. We shall also establish the well-known De Marr's theorem for a family of weak compatible pairs in a hyperconvex metric space [0,1] and show by an example that it fails to hold in general hyperconvex metric spaces.
| Original language | English |
|---|---|
| Article number | 100 |
| Journal | Fixed Point Theory and Algorithms for Sciences and Engineering |
| Volume | 2012 |
| DOIs | |
| State | Published - 2012 |
Bibliographical note
Funding Information:The authors would like to thank the referees for their comments that undoubtedly helped us to improve the text. The first author gratefully acknowledges the support from the Deanship of Scientific Research (DSR) at King Abdulaziz University (KAU) during this research.
Keywords
- Continuous retraction
- Hyperconvex metric space
- Nonexpansive mapping
- Uniformly convex metric space
- Weakly compatible pair
ASJC Scopus subject areas
- Geometry and Topology
- Applied Mathematics