Collective fixed points and maximal elements with applications to abstract economies

DOI10.1016/j.jmaa.2004.03.067zbMath1051.54028OpenAlexW2087857028MaRDI QIDQ1877793

Lai-Jiu Lin, Qamrul Hasan Ansari

Publication date: 19 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.03.067

zbMATH Keywords

multivalued maps\(\Phi\)-condensing\(L_S\)-majorized mapsAbstract economiesCollective fixed points theoremsMaximal element theoremsTransfer compactly open valued maps

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) General equilibrium theory (91B50) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10)

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Cites Work

• Unnamed Item
• Unnamed Item
• Existence of maximal elements and equilibria in linear topological spaces
• A fixed point theorem equivalent to the Fan-Knaster-Kuratowski- Mazurkiewicz theorem
• Fixed point theorems for multivalued noncompact acyclic mappings
• Existence of equilibrium actions and of equilibrium. A note on the 'new' existence theorems
• Remarks on fixed points, maximal elements, and equilibria of generalized games
• Coincidence and fixed point theorems with applications
• Selecting families
• Maximal elements of condensing preference maps
• A fixed point theorem and equilibrium point of an abstract economy
• On Nonlinear Variational Inequalities
• The study of maximal elements, fixed points for -majorized mappings and their applications to minimax and variational inequalities in product topological spaces
• A fixed point theorem and its applications to a system of variational inequalities
• New fixed point theorems for a family of mappings and applications to problems on sets with convex sections
• Maximal elements and equilibria for condensing correspondences
• Applications of a fixed point theorem in \(G\)-convex space