Remarks on Caristi's fixed point theorem

Research output: Contribution to journalArticlepeer-review

62 Scopus citations

Abstract

In this work, we give a characterization of the existence of minimal elements in partially ordered sets in terms of fixed points of multivalued maps. This characterization shows that the assumptions in Caristi's fixed point theorem can, a priori, be weakened. Finally, we discuss Kirk's problem on an extension of Caristi's theorem and prove a new positive result which illustrates the weakening mentioned before.

Original languageBritish English
Pages (from-to)227-231
Number of pages5
JournalNonlinear Analysis, Theory, Methods and Applications
Volume71
Issue number1-2
DOIs
StatePublished - 1 Jul 2009

Keywords

  • Contraction and nonexpansive mappings
  • Fixed point
  • Minimal element
  • Multivalued mappings
  • Order preserving mappings
  • Partially ordered sets
  • Subadditive functions

Fingerprint

Dive into the research topics of 'Remarks on Caristi's fixed point theorem'. Together they form a unique fingerprint.

Cite this