KKM mappings in metric spaces

DOI10.1016/j.na.2004.10.003zbMath1076.47043OpenAlexW2090068204MaRDI QIDQ1764857

Xianqiang Yang

Publication date: 22 February 2005

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.2004.10.003

zbMATH Keywords

KKM propertyhyperconvex metric spaceFan's matching theoremFan--Browder type theoremFan's best approximation theorem

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25)

Related Items (24)

Knaster-Kuratowski-Mazurkiewicz theorem in generalized metric spaces with applications ⋮ Best Approximation in ℝ-Trees ⋮ Fixed point theorems for generalized set-contraction maps and their applications ⋮ KKM property and fixed point theorems in metric spaces ⋮ Fixed point theorems for the class S-KKM mappings in abstract convex spaces ⋮ Best and coupled best approximation theorems in abstract convex metric spaces ⋮ Some results for the family \(KKM(X,Y)\) and the \(\Phi\)-mapping in \(FC\)-spaces ⋮ Topological aspects of circular metric spaces and some observations on the KKM property towards quasi-equilibrium problems ⋮ KKM mappings in cone \(b\)-metric spaces ⋮ Improving KKM theory on general metric type spaces ⋮ Unnamed Item ⋮ Generalized KKM theorems on hyperconvex metric spaces and some applications ⋮ Some results for the family 2-gKKM\((X,Y)\) and the \(\Phi\)-mapping in hyperconvex metric spaces ⋮ Diametrically contractive multivalued mappings ⋮ Unnamed Item ⋮ KKM mappings in metric type spaces ⋮ Fixed points of nearly quasi-closed and nearly almost convex mappings ⋮ Best proximity pairs theorems for continuous set-valued maps ⋮ Fixed point theorems for a \(k\)-set contraction in a metric space ⋮ The 2-KKM property and its applications in hyperconvex metric spaces ⋮ Fixed point theorems for a weaker Meir-Keeler type \(\psi \)-set contraction in metric spaces ⋮ Unnamed Item ⋮ Generalized 2-\(_gKKM\) property in a hyperconvex metric space and its applications ⋮ KKM mappings in cone metric spaces and some fixed point theorems

Cites Work

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• Continuous selections. I
• Extension of uniformly continuous transformations and hyperconvex metric spaces
• A generalization of Tychonoff's fixed point theorem
• 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
• Fixed point theory for \(k\)-CAR sets
• KKM property and fixed point theorems
• Fixed point theorems of upper semicontinuous multivalued mappings with applications in hyperconvex metric spaces
• Some selection theorems without convexity
• The Knaster--Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications
• Fixed points theorems and quasi-variational inequalities in \(G\)-convex spaces
• Fixed point theorems in hyperconvex metric spaces
• Hyperconvex spaces revisited
• An Introduction to Metric Spaces and Fixed Point Theory

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