Fan-Browder Fixed Point Theorem Research Articles

Strict Vector Equilibrium Problems of Multi-Product Supply–Demand Networks with Capacity Constraints and Uncertain Demands

This paper considers a multi-product, multi-criteria supply–demand network equilibrium model with capacity constraints and uncertain demands. Strict network equilibrium principles are proposed both in the case of a single criterion and multi-criteria, respectively. Based on a single criterion, it proves that strict network equilibrium flows are equivalent to vector variational inequalities, and the existence of strict network equilibrium flows is derived by virtue of the Fan–Browder fixed point theorem. Based on multi-criteria, the scalarization of strict network equilibrium flows is given by using Gerstewitz’s function without any convexity assumptions. Meanwhile, the necessary and sufficient conditions of strict network equilibrium flows are derived in terms of vector variational inequalities. Finally, an example is given to illustrate the application of the derived theoretical results.

The rise and fall of L-spaces, II

In 2005, Ben-El-Mechaiekh, Chebbi, and Florenzano obtained a generalization of Ky Fan's 1984 KKM theorem on the intersection of a
 family of closed sets on non-compact convex sets in a topological vector space. They also extended the Fan-Browder fixed point theorem
 to multimaps on non-compact convex sets. Since then several groups of the L-space theorists introduced coercivity families and applied
 them to L-spaces, H-spaces, etc. In this article, we show that better forms of such works can be deduced from a general KKM theorem
 on abstract convex spaces in our previous works. Consequently, all of the known KKM theoretic results on L-spaces related coercivity
 families are extended to corresponding better forms on abstract convex spaces.
 
 This article is a continuation of our \cite{38} and a revised and extended version of \cite{34}.

Fixed point theorems in "Equation missing" spaces with applications

Abstract In this paper, noncompact CAT ( 0 ) versions of the Fan-Browder fixed point theorem are established. As applications, we obtain new minimax inequalities, a saddle point theorem, a fixed point theorem for single-valued mappings, best approximation theorems, and existence theorems of φ-equilibrium points for multiobjective noncooperative games in the setting of noncompact CAT ( 0 ) spaces. These results generalize many well-known theorems in the literature. MSC:91A10, 47H04, 47H10, 54H25.

Class𝔄-KKM(X,Y,Z), GeneralKKMType Theorems, and Their Applications in Topological Vector Space

The class𝔄-KKM(X,Y,Z)and generalizedKKMmapping are introduced, and some generalizedKKMtheorems are proved. As applications, Ky Fan’s matching theorem and Fan-Browder fixed-point theorem are extended, and some existence theorems of solutions for the generalized vector equilibrium problems are established under noncompact setting, which improve and generalize some known results.

Existence Results for Strong Mixed Vector Equilibrium Problem for Multivalued Mappings

We consider a strong mixed vector equilibrium problem in topological vector spaces. Using generalized Fan-Browder fixed point theorem (Takahashi 1976) and generalized pseudomonotonicity for multivalued mappings, we provide some existence results for strong mixed vector equilibrium problem without using KKM-Fan theorem. The results in this paper generalize, improve, extend, and unify some existence results in the literature. Some special cases are discussed and an example is constructed.

Existence theorems of an extension for generalized strong vector quasi-equilibrium problems

In this paper, we study generalized strong vector quasi-equilibrium problems in topological vector spaces. Using the generalization of Fan-Browder fixed point theorem, we provide existence theorems for an extension of generalized strong vector quasi-equilibrium problems with and without monotonicity. The results in this paper generalize, extend and unify some well-known existence theorems in literature.

Minimax Problems for Set-Valued Mappings

In this article, by virtue of the Fan-Browder fixed point theorem, we first obtain a minimax theorem and establish an equivalent relationship between the minimax theorem and a cone saddle point theorem for scalar set-valued mappings. Then, by using scalarization functions, we investigate an existence theorem of the cone saddle point for set-valued mappings. Simultaneously, we also establish a minimax theorem for set-valued mappings.

An Extension of a Generalized Equilibrium Problem

In this note, we consider a multi-valued version of a generalized system (GS) called the multi-valued generalized system (MGS). Using the Fan-Browder fixed point theorem and Brouwer’s fixed point theorem as basic tools, we provide existence theorems on (MGS) with and without monotonicity, respectively.

R-KKM Theorems in FC-Metric Spaces with Applications to Variational Inequalities and Fixed Points

In this paper,the FC-metric space is introduced and an R-KKM theorem is established for noncompact FC-metric spaces.As applications,the properties of the solution set of variational inequalities,intersection point set,Ky Fan section and the maximal element set are shown,and a Fan-Browder fixed point theorem in FC-metric spaces is obtained.

Variational relation problems and equivalent forms of generalized Fan-Browder fixed point theorem with applications to Stampacchia equilibrium problems

In this paper, we study the existence theorems of solution for variational relation problems. From the existence theorems of solution for variational relation problems, we study equivalent forms of generalized Fan-Browder fixed point theorem, existence theorems of solutions for Stampacchia vector equilibrium problems and generalized Stampacchia vector equilibrium problems. Our results contains many orginal results and have many applications in Nonlinear Analysis.

New generalizations of basic theorems in the KKM theory

In the present paper, we obtain a new KKM type theorem for intersectionally closed-valued KKM maps and some useful new basic consequences. Typical examples of them are abstract forms of Fan’s matching theorem, Fan’s geometric lemma, the Fan–Browder fixed point theorem, maximal element theorems, Fan’s minimax inequality, variational inequalities, and others.

Existence and Stability of Solutions for Implicit Multivalued Vector Equilibrium Problems

A class of implicit multivalued vector equilibrium problems is studied. By using the generalized Fan-Browder fixed point theorem, some existence results of solutions for the implicit multivalued vector equilibrium problems are obtained under some suitable assumptions. Moreover, a stability result of solutions for the implicit multivalued vector equilibrium problems is derived. These results extend and unify some recent results for implicit vector equilibrium problems, multivalued vector variational inequality problems, and vector variational inequality problems.

On Generalized Implicit Vector Equilibrium Problems in Topological Ordered Spaces

We discuss three classes of generalized implicit vector equilibrium problems in topological ordered spaces. Under some conditions, we prove three new existence theorems of solutions for the generalized implicit vector equilibrium problems in topological ordered spaces by using the Fan-Browder fixed point theorem.

A new KKM theorem in L-convex spaces and some applications

In this paper, a new KKM theorem is established in L-convex spaces. As applications, a Ky Fan matching theorem for compactly open covers, a Fan–Browder coincidence theorem, a Fan–Browder fixed point theorem and a maximal element theorem are obtained in L-convex spaces. These theorems unify, improve and generalize some recent results in the references therein. Finally, the equilibrium existence theorems for abstract economies and qualitative games in L-convex spaces are yielded.

Fixed points, coincidence points and maximal elements with applications to generalized equilibrium problems and minimax theory

In this paper, using a generalization of the Fan–Browder fixed point theorem, we obtain a new fixed point theorem for multivalued maps in generalized convex spaces from which we derive several coincidence theorems and existence theorems for maximal elements. Applications of these results to generalized equilibrium problems and minimax theory will be given in the last sections of the paper.

The applications of the Fan–Browder fixed point theorem in topological ordered spaces

In this work, for topological ordered spaces, by using the Fan–Browder fixed point theorem, we obtain existence results for solutions for some generalized quasi-Ky Fan inequalities and Nash equilibrium points for a game system.

Note on KKM maps and applications

We apply the KKM technique to study fixed point theory, minimax inequality and coincidence theorem. Some new results on Fan-Browder fixed point theorem, Fan's minimax theorem and coincidence theorem are obtained.

New versions of the Fan-Browder fixed point theorem and existence of economic equilibria

We introduce a generalized form of the Fan-Browder fixed point theorem and apply to game-theoretic and economic equilibrium existence problem under the more generous restrictions. Consequently, we state some of recent results of Urai (2000) in more general and efficient forms.

New topological versions of the Fan–Browder fixed point theorem

New topological versions of the Fan–Browder fixed point theorem

On some equilibrium problems for multimaps

In this paper, we first establish the continuity property for multimaps and generalized Berge's theorem for multimaps. Then we apply these results, and the Fan–Browder fixed point theorem to establish the existence theorems of quasi-equilibrium problems and generalized quasi-equilibrium problems for multimaps.