Comments on some fixed point theorems in hyperconvex metric spaces.

DOI10.1016/j.jmaa.2003.10.022zbMath1069.47061OpenAlexW1985952237MaRDI QIDQ1426071

Sehie Park, Jeong-Heon Kim

Publication date: 14 March 2004

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2003.10.022

zbMATH Keywords

fixed pointKKM theoremadmissible setgeneralized convex spacehyperconvex metric spaceacyclic mapFan--Browder type mapLC-metric space

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items (7)

A unified fixed point theory in generalized convex spaces ⋮ Best and coupled best approximation theorems in abstract convex metric spaces ⋮ Fixed point theory of multimaps in abstract convex uniform spaces ⋮ Best approximation and fixed point theorems in hyperconvex metric spaces ⋮ Best proximity pairs for upper semicontinuous set-valued maps in hyperconvex metric spaces ⋮ Coincidence point, best approximation, and best proximity theorems for condensing set-valued maps in hyperconvex metric spaces ⋮ Approximate fixed point theorems for the class of almost S-KKM\(_{\mathcal C}\) mappings in abstract convex uniform spaces

Cites Work

• Extension of uniformly continuous transformations and hyperconvex metric spaces
• Contractibility and generalized convexity
• The characterization of generalized metric KKM mappings with open values in hyperconvex metric spaces and some applications
• Extension and selection theorems in topological spaces with a generalized convexity structure
• KKM and Ky Fan theorems in hyperconvex metric spaces
• Foundations of the KKM theory on generalized convex spaces
• Generalizations of the KKM type theorems on generalized convex spaces
• Fixed point theorems of upper semicontinuous multivalued mappings with applications in hyperconvex metric spaces
• New topological versions of the Fan-Browder fixed point theorem.
• Some selection theorems without convexity
• Coincidence theorems for admissible multifunctions on generalized convex spaces
• The Knaster--Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications
• Six theorems about injective metric spaces
• On nonlinear contraction semigroups in sup norm spaces
• Existence of Fixed Points of Nonexpansive Mappings in Certain Banach Lattices
• Fixed point theorems in hyperconvex metric spaces
• Continuous Selection Theorems in Generalized Convex Spaces
• Fixed point theorems in locally H-convex uniform spaces
• Continuous mappings in compact hyperconvex metric spaces
• Some applications of the Knaster-Kuratowski and Mazurkiewicz principle in hyperconvex metric spaces
• Fixed point theorems in locally \(G\)-convex spaces
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