Simplicial convexity and its applications

DOI10.1016/0022-247X(87)90148-XzbMath0638.52002MaRDI QIDQ1099411

Roger Bielawski

Publication date: 1987

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

zbMATH Keywords

surveyfixed point theorycontinuous selectionsminimax principleabsolute retractsMichael familyequilibrium theoremfinitely local convexityKnaster-Kuratowski-Mazurkiewicz mapsKy Fan coincidence theoremS-convexitysimplicial convexity

Mathematics Subject Classification ID

Axiomatic and generalized convexity (52A01) Selections in general topology (54C65) Fixed-point and coincidence theorems (topological aspects) (54H25) Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) (54C55)

Related Items (22)

Collectively fixed point theorems in noncompact abstract convex spaces with applications ⋮ Abstract Convexity, Some Relations and Applications ⋮ Generalizations of the Nash equilibrium theorem in the KKM theory ⋮ A unified fixed point theory in generalized convex spaces ⋮ Foundations of the KKM theory on generalized convex spaces ⋮ A united approach to generalization of the KKM-type theorems related to acyclic maps ⋮ A more refined convexity idea for Nash equilibria ⋮ Spaces and maps approximation and fixed points ⋮ Generalized variational inequalities and equilibrium problems in generalized convex spaces ⋮ Generalized convexity and applications to fixed points and equilibria ⋮ Compressibility: A property of topological spaces related to abstract convexity ⋮ G-KKM theorem, minimax inequalities and saddle points ⋮ On continuous choice of retractions onto nonconvex subsets ⋮ Dependency relations ⋮ Applications of general infimum principles to fixed-point theory and game theory ⋮ Fixed points of contractive multivalued maps ⋮ Abstract convexity and fixed points ⋮ Existence of equilibrium in generalized games with abstract convexity structure ⋮ Nonconvexity in problems of multivalued calculus ⋮ Fixed points of upper semicontinuous mappings in locally G-convex spaces ⋮ Contractibility and generalized convexity ⋮ Continuous selection theorem, coincidence theorem, and generalized equilibrium in \(L\)-convex spaces

Cites Work

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• Continuous selections. I
• Continuous selections. II
• On general minimax theorems
• A generalization of Tychonoff's fixed point theorem
• Applications of a theorem concerning sets with convex sections
• Non-cooperative games
• Convex Structures and Continuous Selections
• A Fixed Point Theory for Multi-Valued Mappings
• Convexity on a topological space
• Retracts in Metric Spaces
• Locally equiconnected spaces and absolute neighborhood retracts

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