A selection theorem and its applications

DOI10.1017/S0004972700011849zbMath0762.47030MaRDI QIDQ3993946

Won Kyu Kim, Xie Ping Ding, Kok-Keong Tan

Publication date: 13 August 1992

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

intersection theoremequilibrium existence theoremsfixed point theorem in a non-compact product spacenon-compact abstract economyYannelis-Prabhakov's theorem on continuous selectors

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Fixed-point theorems (47H10) General equilibrium theory (91B50) Convex sets in topological vector spaces (aspects of convex geometry) (52A07)

Related Items (56)

Existence of solution and algorithms for a class of bilevel variational inequalities with hierarchical nesting structure ⋮ Continuous Selection Theorems in Generalized Convex Spaces ⋮ Approximate selection theorems and their applications ⋮ Continuous selection, collectively fixed points and system of coincidence theorems in product topological spaces ⋮ Collectively coincidence-type results and applications ⋮ Continuous selecting families and collectively fixed point theory ⋮ Majorized multivalued maps, equilibrium and coincidence points in the topological vector space setting ⋮ On equilibrium problem of abstract economy, generalized quasi-variational inequality, and an optimization problem in locally \(H\)-convex spaces ⋮ New collectively fixed point theorems and applications in \(G\)-convex spaces ⋮ Levitin-Polyak well-posedness by perturbations for systems of set-valued vector quasi-equilibrium problems ⋮ Classes of maps with continuous selections and generalized games ⋮ Unnamed Item ⋮ Collectively coincidence results and selecting families ⋮ Fixed point and maximal element theorems with applications to abstract economies and minimax inequalities ⋮ A new fixed point theorem and its applications ⋮ Coincidence results and Leray-Schauder alternatives between multivalued maps with continuous selections and admissible maps ⋮ A noncompact generalized quasi-variational inequality ⋮ The study of abstract economies with two constraint correspondences ⋮ Selecting families and their applications ⋮ Continuation methods for closed, weakly closed, DKT, and WDKT maps ⋮ An essential map approach for multivalued \(A\)-proper, weakly inward, DKT and weakly closed maps ⋮ Coincidences for \(DKT\) maps in Fréchet spaces and minimax inequalities. ⋮ Single and twin coincidence points for multivalued maps in Fréchet spaces ⋮ Fixed points, minimax inequalities and equilibria of noncompact abstract economies in \(FC\)-spaces ⋮ Quasi-Equilibrium Problems and Fixed Point Theorems of Separately l.s.c and u.s.c Mappings ⋮ Collectively fixed point and maximal element theorems in topological semilattice spaces ⋮ Continuous selection theorems for Fan-Browder mappings in topological spaces and their applications ⋮ Compact Browder maps and equilibria of abstract economies ⋮ Equilibria of non-compact generalized games with \( L^*\)-majorized preference correspondences ⋮ Unnamed Item ⋮ Generalized vector variational like inequalities in fuzzy environment ⋮ Existence of a solution for generalized vector variational inequalities ⋮ A note on equilibria for abstract economies ⋮ Fixed-point theory for set valued mappings between topological vector spaces having sufficiently many linear functionals ⋮ Equilibria of lower semicontinuous games ⋮ Variational inequalities, coincidence theory, and minimax inequalities ⋮ Fixed point theorems on product topological spaces and applications ⋮ Generalized fuzzy games and fuzzy equilibria ⋮ Generalized vector \(F\)-variational inequalities and vectorf-complementarity problems for point-to-set mappings ⋮ Continuous selections and fixed points of multi-valued mappings on noncompact or nonmetrizable spaces ⋮ A general coincidence theory for set-valued maps ⋮ A new equilibrium existence theorem for abstract fuzzy economies ⋮ Equilibria of noncompact generalized games with \(\mathcal U\)-majorized preference correspondences ⋮ Gap functions and existence of solutions to set-valued vector variational inequalities ⋮ A new continuous selection theorem ⋮ Continuation theorems for Mönch countable compactness-type set-valued maps ⋮ Quasiequilibrium problem in \(H\)-spaces ⋮ Some new equilibrium theorems for abstracts economies ⋮ Equilibrium of abstract economy and generalized quasi-variational inequality in \(H\)-spaces ⋮ Existence of equilibrium for generalized abstract fuzzy economies ⋮ Modular best proximity and equilibrium pairs in free generalized games ⋮ A New Generalization of Browder Fixed Point Theorem with Applications ⋮ Equilibria for abstract economies in Hausdorff topological vector spaces ⋮ Remarks on generalized quasi-equilibrium problems ⋮ A new equilibrium existence theorem of generalized game ⋮ Gap functions and existence of solutions to generalized vector variational inequalities

Cites Work

• Unnamed Item
• Unnamed Item
• Existence of maximal elements and equilibria in linear topological spaces
• Non-compact sets with convex sections
• Equilibrium in abstract economies without ordered preferences
• Existence of equilibrium actions and of equilibrium. A note on the 'new' existence theorems
• The fixed point theory of multi-valued mappings in topological vector spaces
• A fixed point theorem and equilibrium point of an abstract economy
• Fixed points for Kakutani factorizable multifunctions
• Fixed-point and Minimax Theorems in Locally Convex Topological Linear Spaces
• A Note on Paracompact Spaces

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