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 | British English |
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Article number | 100 |
Journal | Fixed Point Theory and Applications |
Volume | 2012 |
DOIs | |
State | Published - 2012 |
Keywords
- Continuous retraction
- Hyperconvex metric space
- Nonexpansive mapping
- Uniformly convex metric space
- Weakly compatible pair