Remarks on Caristi's fixed point theorem

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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
Issue number1-2
StatePublished - 1 Jul 2009


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


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