A generalization of Tychonoff's fixed point theorem

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Publication:772593

DOI10.1007/BF01353421zbMath0093.36701WikidataQ116689760 ScholiaQ116689760MaRDI QIDQ772593

Ky Fan

Publication date: 1961

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/160834


zbMATH Keywords

topology



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the existence of maximal elements via the uncovered set ⋮ Fixed point theorems for weakly inward multivalued maps on a \(CAT(0)\) space ⋮ KKM mappings in cone \(b\)-metric spaces ⋮ An extension of the Fitzpatrick theory ⋮ Equilibrium problems in Hadamard manifolds ⋮ A fixed-point theorem and equilibria of abstract economies with weakly upper semicontinuous set-valued maps ⋮ A common fixed point theorem with applications ⋮ Multivalued variational inequalities and coincidence point results ⋮ Densely defined equilibrium problems ⋮ Existence results for vector equilibrium problems given by a sum of two functions ⋮ Exponential type vector variational-like inequalities and nonsmooth vector optimization problems ⋮ Construction of a common element for the set of solutions of fixed point problems and generalized equilibrium problems in Hilbert spaces ⋮ Variational-like inequalities for weakly relaxed \(\eta\)-\(\alpha\) pseudomonotone set-valued mappings in Banach space ⋮ Auxiliary principle technique and iterative algorithm for a perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems ⋮ Extended new generalized mixed vector variational-like inequalities in reflexive Banach spaces ⋮ Generalized vector variational like inequalities in fuzzy environment ⋮ A section theorem with applications to coincidence theorems and minimax inequalities in \(FWC\)-spaces ⋮ New generalizations of basic theorems in the KKM theory ⋮ Political equilibria with electoral uncertainty ⋮ Boundedness and nonemptiness of solution sets for set-valued vector equilibrium problems with an application ⋮ Existence and stability of solutions for implicit multivalued vector equilibrium problems ⋮ Solving the set equilibrium problems ⋮ Generalized vector implicit quasi complementarity problems ⋮ A unifying pair of Cournot-Nash equilibrium existence results ⋮ Existence of equilibria for multivalued mappings and its application to vectorial equilibria ⋮ Regularized equilibrium problems with application to noncoercive hemivariational inequalities. ⋮ Generalized KKM theorems and common fixed point theorems ⋮ Approximate fixed point theorems for the generalized \(\varPsi \)-set contraction mappings on an almost \(\varPhi \)-space ⋮ On a generalized hemivariational inequality on Banach spaces ⋮ Minimax theorems in fuzzy metric spaces ⋮ Existence theorem and algorithm for a general implicit variational inequality in Banach space ⋮ A generalized mixed vector variational-like inequality problem ⋮ Solvability of vector Ky Fan inequalities with applications ⋮ On bilevel variational inequalities ⋮ On the use of KKM multifunctions in fixed point theory and related topics ⋮ Multivalued mappings ⋮ Existence of maximal elements and equilibria in linear topological spaces ⋮ On the existence of equilibria in economies with infinitely many commodities and without ordered preferences ⋮ Social equilibrium and cycles on compact sets ⋮ Extensions of two fixed point theorems of Ky Fan ⋮ Contractibility and generalized convexity ⋮ On a form of KKM principle and SupInfSup inequalities of von Neumann and of Ky Fan type ⋮ Gap functions and existence of solutions to generalized vector variational inequalities ⋮ Existence results for generalized nonlinear variational inclusions ⋮ Generalized vector equilibrium problems for pseudomonotone multivalued bifunctions ⋮ Equilibrium problems in the quasimonotone case ⋮ S-G-L-KKM theorems in L-convex space and their applications to minimax inequalities ⋮ Lower semicontinuity of the efficient solution mapping in semi-infinite vector optimization ⋮ Extended vector Ky Fan inequality ⋮ Extragradient method and golden ratio method for equilibrium problems on Hadamard manifolds ⋮ Fixed Point Theorem and Related Nonlinear Analysis by the Best Approximation Method in p-Vector Spaces ⋮ Stability of the set of solutions for generalized vector equilibrium problems with cone constraints ⋮ A unified study of existence theorems in topologically based settings and applications in optimization ⋮ Exponential augmented Lagrangian methods for equilibrium problems ⋮ Split Equilibrium Problems for Related Games and Applications to Economic Theory ⋮ Unnamed Item ⋮ Approximate Fixed Point Theory for Countably Condensing Maps and Multimaps and Applications ⋮ New hybrid algorithms for global minimization of common best proximity points of some generalized nonexpansive mappings ⋮ Weak KKM set-valued mappings in hyperconvex metric spaces ⋮ Inertial Extragradient Method for Solving Variational Inequality and Fixed Point Problems of a Bregman Demigeneralized Mapping in a Reflexive Banach Spaces ⋮ Topological results, Rothe's principle and Leray-Schauder alternative for the fixed point equation in \(p\)-vector spaces ⋮ Intersection theorems for generalized weak KKM set‐valued mappings with applications in optimization ⋮ Generalized vector quasi-variational-like inequality problem: a new approach ⋮ Unnamed Item ⋮ A topological approach for vector quasi-variational inequalities with set-valued functions ⋮ Nonlinear analysis in \(p\)-vector spaces for single-valued 1-set contractive mappings ⋮ Tikhonov regularization for a class of generalized hemivariational inequality in Banach spaces ⋮ Interval variational inequalities and their relationship with interval optimization problems ⋮ Mixed invex equilibrium problems with generalized relaxed monotone and relaxed invariant pseudomonotone mappings ⋮ On constrained generalized games with action sets in non-locally-convex and non-Hausdorff topological vector spaces ⋮ Multicriteria equilibrium programming: Extraproximal methods ⋮ Efficiencies and Pareto efficiencies of set-valued mappings on ordered spaces ⋮ A new approach about equilibrium problems via Busemann functions ⋮ Semi-infinite interval equilibrium problems: optimality conditions and existence results ⋮ On vector variational \(E\)-inequalities and differentiable vector optimization problem ⋮ Set-valued equilibrium problems based on the concept of null set with applications ⋮ Existence Results of a Generalized Mixed Exponential Type Vector Variational-Like Inequalities ⋮ Applications of Optimization Theory to Social Benefit Maximizations in Macroeconomics with Uncertainty ⋮ Unnamed Item ⋮ Pre-vector variational inequalities ⋮ Strict feasibility for generalized mixed variational inequality in reflexive Banach spaces ⋮ Making Augmented Lagrangian Methods Computer Amenable for Equilibrium Problems ⋮ Split equilibrium problems for related games and applications to economic theory ⋮ Implicit vector equilibrium problems via nonlinear scalarisation ⋮ The Solvability of Nonlinear Split Ordered Variational Inequality Problems in Partially Ordered Vector Spaces ⋮ A general iterative algorithm for vector equilibrium problem ⋮ Generalized variational inequalities and generalized quasi-variational inequalities ⋮ Quasi-Equilibrium Problems and Fixed Point Theorems of Separately l.s.c and u.s.c Mappings ⋮ General theorems of the Knaster-Kuratowski- Mazurkiewicz type and applications to the existence study in optimization ⋮ Densely relaxed pseudomonotone and quasimonotone generalized variational-like inequalities ⋮ Existence theorems via duality for equilibrium problems with trifunctions ⋮ Coalitions and Catastrophic Climate Change ⋮ Duality and gap function for generalized multivalued ϵ-vector variational inequality ⋮ Invariant subspaces of certain linear operators ⋮ Existence results for densely pseudomonotone variational inequalities ⋮ On generalized vector equilibrium problems ⋮ Some applications of the Knaster-Kuratowski and Mazurkiewicz principle in hyperconvex metric spaces ⋮ Unnamed Item ⋮ Relatively monotone variational inequalities over product sets ⋮ A generalization of Minty's lemma and its applications to generalized mixed vector equilibrium problems ⋮ Existence of equilibria for generalized games and generalized social systems with coordination ⋮ Existence conditions in variational inclusions with constraints ⋮ Iterative schemes for solving mixed variational-like inequalities ⋮ On Minimax Inequalities in Topological Spaces Without Convexity Structure ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Existence and duality of generalized vector equilibrium problems ⋮ Best proximity point for proximal Berinde nonexpansive mappings on starshaped sets ⋮ Unified Approaches to Nonlinear Optimization ⋮ Existence results for different type of generalized vector equilibrium problems ⋮ Some eigenvector theorems proved by a Fan-KKM theorem ⋮ Competitive equilibrium:walras meets darwin ⋮ Quasimonotone individual demand ⋮ Existence of a solution and variational principles for vector equilibrium problems ⋮ Fixed point theorems in locally \(G\)-convex spaces ⋮ Some deterministic and random vector equilibrium problems ⋮ On vector variational inequalities ⋮ On vector variational inequalities ⋮ Generalized vector equilibrium problem with pseudomonotone mappings ⋮ A generalization of Browder's fixed point theorem with applications ⋮ A generalization of Browder's fixed point theorem with applications ⋮ On the existence and approximation of solutions for bilevel vector variational inequalities in Banach spaces ⋮ Tikhonov type regularization methods for inverse mixed variational inequalities ⋮ Fixed point theorems in homotopically trivial spaces ⋮ Vectorial form of Ekeland variational principle with applications to vector equilibrium problems ⋮ A general coincidence theorem on contractible spaces ⋮ On the existence problem of solutions to a class of fuzzy mixed exponential vector variational inequalities ⋮ The generalised f-projection operator with an application ⋮ Versions of the Weierstrass Theorem for Bifunctions and Solution Existence in Optimization ⋮ On Continuous Selection Problems for Multivalued Mappings with the Local Intersection Property in Hyperconvex Metric Spaces ⋮ The continuous-time problem with interval-valued functions: applications to economic equilibrium ⋮ Existence and generic stability of solutions for multiclass multicriteria traffic equilibrium problems with capacity constraints of arcs ⋮ Unified forms of fixed point theorems and minimax inequalities ⋮ An extension of Tychonoff’s fixed point theorem to pseudonorm adjoint topological vector spaces ⋮ Nonself KKM Maps and Corresponding Theorems in Hadamard Manifolds ⋮ Existence of solutions for a vector saddle point problem ⋮ A Fixed Point Theorem for Multifunctions in a Locally Convex Space ⋮ A class of generalized operator equilibrium problems ⋮ Nonsmooth quasi-variational-like inequalities with applications to nonsmooth vector quasi-optimization ⋮ Best Approximation in Nonlinear Functional Analysis ⋮ On generalized implicit operator equilibrium problems ⋮ Existence results for equilibrium problems with applications to evolution equations



Cites Work

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