Abstract Convexity, Some Relations and Applications

DOI10.1080/0233193021000015587zbMath1037.52001OpenAlexW2030556656MaRDI QIDQ4805777

Juan-Vicente Llinares

Publication date: 2002

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: http://www.cepremap.fr/depot/couv_orange/co9803.pdf

zbMATH Keywords

fixed pointsabstract convexitymaximal elementsKKM Lemma

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Axiomatic and generalized convexity (52A01) Fixed-point and coincidence theorems (topological aspects) (54H25) Fixed points and coincidences in algebraic topology (55M20)

Related Items (13)

Convexity with respect to families of sections and lines and their application in optimization ⋮ Fixed point theorems for the class S-KKM mappings in abstract convex spaces ⋮ An envelope operator for full convexity to define polyhedral models in digital spaces ⋮ Full convexity for polyhedral models in digital spaces ⋮ Properties of extremal families of \(MN\)-convex (\(MN\)-concave) functions ⋮ Preferences in Abstract Convex Structures ⋮ On M-fuzzifying JHC convex structures and M-fuzzifying Peano interval spaces ⋮ Convex hesitant fuzzy sets ⋮ Second-order set-valued differential equations with boundary conditions ⋮ L-FUZZY CONVEXITY INDUCED BY L-CONVEX FUZZY SUBLATTICE DEGREE ⋮ Aggregation of convex intuitionistic fuzzy sets ⋮ Poset valued convexities ⋮ Approximate fixed point theorems for the class of almost S-KKM\(_{\mathcal C}\) mappings in abstract convex uniform spaces

Cites Work

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• Contractibility and generalized convexity
• Geodesic convexity in nonlinear optimization
• Simplicial convexity and its applications
• Compressibility: A property of topological spaces related to abstract convexity
• The Kakutani property and the fixed point property of topological spaces with abstract convexity
• Abstract convexity and fixed points
• Unified treatment of the problem of existence of maximal elements in binary relations: A characterization
• Maximal elements and fixed points for binary relations on topological ordered spaces
• Convex Structures and Continuous Selections
• A survey of recent[1985-1995advances in generalized convexity with applications to duality theory and optimality conditions]
• Axioms for convexity

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