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Zbl 1175.54056
Khamsi, M.A.
Remarks on Caristi's fixed point theorem. (English)
[J] Nonlinear Anal., Theory Methods Appl. 71, No. 1-2, A, 227-231 (2009). ISSN 0362-546X

Summary: 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.

MSC 2000:: *54H25 Fixed-point theorems in topological spaces
54E50 Complete metric spaces
06A06 Partial order
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: partially ordered sets; minimal element; order-preserving mappings; contraction and nonexpansive mappings; fixed point; multivalued mappings; subadditive functions

Cited in: Zbl pre06150142 Zbl 1201.54036

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