Remarks on Caristi's fixed point theorem and Kirk's problem

DOI10.1016/j.na.2010.07.048zbMath1201.54036OpenAlexW1983967719MaRDI QIDQ607091

Zhilong Li

Publication date: 19 November 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.07.048

zbMATH Keywords

Caristi's fixed point theoremCaristi type mappingKhamsi's fixed point theoremKirk's problem

Mathematics Subject Classification ID

Partial orders, general (06A06) Fixed-point and coincidence theorems (topological aspects) (54H25)

Related Items

Maximal and minimal point theorems and Caristi's fixed point theorem ⋮ On fixed point theory of monotone mappings with respect to a partial order introduced by a vector functional in cone metric spaces ⋮ On Caristi's fixed point theorem and completeness of probabilistic metric spaces ⋮ New results for set-valued mappings on ordered metric spaces ⋮ Fixed point theorems in partially ordered complete metric spaces ⋮ Largest and least fixed point theorems of increasing mappings in partially ordered metric spaces ⋮ Fixed point theorems of set-valued mappings in partially ordered Hausdorff topological spaces ⋮ On Caristi type maps and generalized distances with applications ⋮ Fixed points of set-valued Caristi-type mappings on semi-metric spaces via partial order relations

Cites Work

• Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings
• Remarks on Caristi's fixed point theorem
• A generalization of Caristi's theorem with applications to nonlinear mapping theory
• Caristi's fixed point theorem and selections of set-valued contractions
• Converses to fixed point theorems of Zermelo and Caristi
• Fixed Point Theorems for Mappings Satisfying Inwardness Conditions
• Caristi's fixed point theorem and metric convexity
• On Nonlinear Contractions
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