Nonexpansive retracts and weak compatible pairs in metric Spaces

N. Hussain, G. Jungck, M. A. Khamsi

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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 languageBritish English
Article number100
JournalFixed Point Theory and Applications
Volume2012
DOIs
StatePublished - 2012

Keywords

  • Continuous retraction
  • Hyperconvex metric space
  • Nonexpansive mapping
  • Uniformly convex metric space
  • Weakly compatible pair

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