On externally complete subsets and common fixed points in partially ordered sets

Mohammad Z. Abu-Sbeih, Mohamed A. Khamsi

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this study, we introduce the concept of externally complete ordered sets. We discuss the properties of such sets and characterize them in ordered trees. We also prove some common fixed point results for order preserving mappings. In particular, we introduce for the first time the concept of Banach Operator pairs in partially ordered sets and prove a common fixed point result which generalizes the classical De Marr ' s common fixed point theorem.

Original languageBritish English
Article number97
JournalFixed Point Theory and Applications
Volume2011
DOIs
StatePublished - Dec 2011

Keywords

  • Fixed point
  • Hyperconvex metric spaces
  • Order preserving mappings
  • Order trees
  • Partially ordered sets

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