Comments on abstract convexity structures on topological spaces

DOI10.1016/j.na.2009.06.100zbMath1183.52001OpenAlexW2061136331MaRDI QIDQ1049011

Sehie Park

Publication date: 8 January 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.2009.06.100

zbMATH Keywords

abstract convex spaceH-conditiongeneralized (\(G\)-) convex spaceH\(_{0}\)-condition

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Axiomatic and generalized convexity (52A01)

Related Items (1)

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Cites Work

• Generalized KKM type theorems in FC-spaces with applications. I
• Some properties of abstract convexity structures on topological spaces
• Abstract convexity and fixed points
• Unified treatment of the problem of existence of maximal elements in binary relations: A characterization
• Maximal element theorems in product \(FC\)-spaces and generalized games
• New topological versions of the Fan-Browder fixed point theorem.
• Some selection theorems without convexity
• A unified fixed point theory in generalized convex spaces
• From a KKM theorem to Nash equilibria in \(L\)-spaces
• The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities
• The matching theorems and coincidence theorems for generalized R-KKM mapping in topological spaces
• A further characteristic of abstract convexity structures on topological spaces
• Continuous Selection Theorems in Generalized Convex Spaces
• ELEMENTS OF THE KKM THEORY ON CONVEX SPACES
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