Best approximation and fixed point theorems in hyperconvex metric spaces

DOI10.1016/j.na.2005.02.063zbMath1224.54094OpenAlexW2074174149MaRDI QIDQ999984

Jack T. Markin

Publication date: 4 February 2009

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.2005.02.063

zbMATH Keywords

fixed pointadmissible setbest approximationexternally hyperconvex sethyperconvex space

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Fixed-point and coincidence theorems (topological aspects) (54H25) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (6)

Common fixed points for commuting mappings in hyperconvex spaces ⋮ Invariant approximations for commuting mappings in CAT(0) and hyperconvex spaces ⋮ Best approximation theorems for nonexpansive and condensing mappings in hyperconvex spaces ⋮ Coincidence point, best approximation, and best proximity theorems for condensing set-valued maps in hyperconvex metric spaces ⋮ Invariant approximations in CAT(0) spaces ⋮ Generalized 2-\(_gKKM\) property in a hyperconvex metric space and its applications

Cites Work

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• Extension of uniformly continuous transformations and hyperconvex metric spaces
• KKM and Ky Fan theorems in hyperconvex metric spaces
• Comments on some fixed point theorems in hyperconvex metric spaces.
• Fixed point theorems of upper semicontinuous multivalued mappings with applications in hyperconvex metric spaces
• The Knaster--Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications
• A best approximation theorem for nonexpansive set-valued mappings in hyperconvex metric spaces
• Fixed point theorems in hyperconvex metric spaces
• Fixed point and selection theorems in hyperconvex spaces
• Hyperconvexity and Nonexpansive Multifunctions
• Some applications of the Knaster-Kuratowski and Mazurkiewicz principle in hyperconvex metric spaces

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