Remarks on Caristi's fixed point theorem

M. A. Khamsi

doi:10.1016/j.na.2008.10.042

Remarks on Caristi's fixed point theorem

M. A. Khamsi

Mathematics

Research output: Contribution to journal › Article › peer-review

63 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 language	British English
Pages (from-to)	227-231
Number of pages	5
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	71
Issue number	1-2
DOIs	https://doi.org/10.1016/j.na.2008.10.042
State	Published - 1 Jul 2009

Keywords

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

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10.1016/j.na.2008.10.042

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AB - 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.

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KW - Minimal element

KW - Multivalued mappings

KW - Order preserving mappings

KW - Partially ordered sets

KW - Subadditive functions

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Remarks on Caristi's fixed point theorem

Abstract

Keywords

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