Fan Glicksberg Fixed Point Theorem Research Articles

Existence of equilibrium solutions for multi-objective population games with fuzzy parameters

This paper investigates the existence of equilibrium solutions for multi-objective population games with payoff functions involving fuzzy parameters. This paper first puts forward the concepts of α-Pareto-Nash-Slater equilibria and weakly α-Pareto-Nash-Slater equilibria for such games. Furthermore, the existence of α-Pareto-Nash-Slater equilibria is proved by Fan-Glicksberg fixed point theorem and that of weakly α-Pareto-Nash-Slater equilibria is shown by vector-valued Ky Fan inequality. Finally, their feasibility is illustrated by some examples.

Existence and stability of fuzzy Pareto-Nash equilibria for fuzzy constrained multi-objective games with fuzzy payoffs

<abstract><p>A new class of fuzzy constrained multi-objective games with fuzzy payoffs (FCMGFPs) is considered in this paper. First, Berge's maximum theorem for the fuzzy-vector-valued function is obtained. Based on this theorem and the Fan-Glicksberg fixed point theorem, the existence theorem of the fuzzy Pareto-Nash equilibrium for the FCMGFP is established. Second, the abstract rationality function for the FCMGFP is given by using a nonlinear scalarization function of interval vectors. Finally, a series of results, such as structural stability ($ (\gamma, \epsilon) $-stability) and robustness to $ \epsilon $-equilibrium ($ (\gamma, \epsilon) $-robustness), are obtained.</p></abstract>

A class of elliptic quasi-variational–hemivariational inequalities with applications

In this paper we study a class of quasi-variational–hemivariational inequalities in reflexive Banach spaces. The inequalities contain a convex potential, a locally Lipschitz superpotential, and a solution-dependent set of constraints. Solution existence and compactness of the solution set to the inequality problem are established based on the Kakutani–Ky Fan–Glicksberg fixed point theorem. Two examples of the interior and boundary semipermeability models illustrate the applicability of our results.

Existence of solution to n-person noncooperative games and minimax regret equilibria with set payoffs

In this paper, by virtue of the Kakutani–Fan–Glicksberg fixed point theorem and a nonlinear scalarization function, we first obtain an existence theorem of general n-person noncooperative games problems with set payoffs. Then, we also obtain existence theorems of minimax regret equilibria and ϵ-minimax regret equilibria with scalar set payoffs. Some examples are given to illustrate our results.

On multivalued Duffing equation

We present an approach based on the Kakutani–Ky Fan–Glicksberg fixed point theorem and a truncation argument, to prove the existence of strong solutions for two boundary value problems for the Duffing-type ordinary differential equation with multivalued terms. As a special case we recover the original Duffing equation.

Amenability and Fan–Glicksberg theorem for set-valued mappings

In this paper, we begin by discussion of some well known results on the existence of left invariant means in the spaces: LUC(S), AP(S) and W AP(S) with Hahn-Banach extension theorem. We then give a new and precise proof of the well known Fan–Glicksberg fixed point theorem. This is then followed by a discussion on some related open problems.

Fixed Points, Continuous Selections, and Existence of Solution of Optimization-Related Problems

ABSTRACTWe propose a definition of a generalized type of Knaster–Kuratowski–Mazurkiewicz (KKM) mappings, called a weak T-KKM mapping, and a corresponding weak KKM property. A new extension of the Fan–Glicksberg fixed-point theorem is established. Sufficient conditions for the existence of a continuous selection, a fixed point of a composition, and a coincidence point are also provided. Then, we use the obtained results to study the existence of solutions to various optimization-related problems. Discussions and detailed examples are included as well to compare our results with existing ones and to explain their advantages in many situations.

Recursive equilibrium with Price Perfect Foresight and a minimal state space

This paper analyzes general equilibrium models with finite heterogeneous agents who anticipate future prices through a price expectation function with or without accuracy. I show the existence of a recursive equilibrium with a minimal state space through the Kakutani–Fan–Glicksberg fixed point theorem. Moreover, any such recursive equilibrium implements a sequential equilibrium and its uniqueness implies its continuity. Particularly, I prove that an agent making persistent errors in the price expectation function is driven out of the market in any sequential equilibrium implemented by a continuous recursive equilibrium. This result is established under the condition that exogenous variables converge in probability and assuming that the relative variability of all stochastic discount factors is low.

Solvability of a System of Vector Equilibrium Problems Involving Topological Pseudomonotonicity

In this paper, we study the solvability of a system of vector equilibrium problems. We extend the concept of topological pseudomonotonicity to a family of mappings. We prove existence results for the system of vector equilibrium problems under topological pseudomonotonicity conditions by the Kakutani–Fan–Glicksberg fixed point theorem. As applications, we obtain existence results for systems of equilibrium problems under topological pseudomonotonicity conditions.

Generalized KKM theorems and common fixed point theorems

In this paper, we first prove a generalized KKM theorem, and then use this generalized KKM theorem to establish the generalized equi-KKM theorem, common fixed point theorems for a family of multivalued maps, and the Kakutani–Fan–Glicksberg fixed point theorem. We also show that an existence theorem of the common fixed point theorem is equivalent to the Kakutani–Fan–Glicksberg fixed point theorem.

On Lomonosov’s Lemma in normed spaces

In this paper we give a new proof with the Fan-Glicksberg fixed point theorem to a special case of the famous Lomonosov Invariant Subspace Theorem.

A generalized vector variational inequality problem with a set-valued semi-monotone mapping

In this paper, we first generalize the concept of semi-monotonicity for a scalar single-valued mapping to the case of a vector set-valued mapping. Then we consider a generalized vector variational inequality problem concerning the vector set-valued semi-monotone mapping; several existence results are obtained by using the Kakutani–Fan–Glicksberg fixed point theorem which generalize some results for vector variational inequality problems studied in recent years.

Existence and stability of solutions for generalized strong vector quasi-equilibrium problem

In this paper, we study the generalized strong vector quasi-equilibrium problem without assuming that the dual of the ordering cone has a weak ∗ compact base. We establish an existence theorem of solutions for the generalized strong vector quasi-equilibrium problem by using Kakutani–Fan–Glicksberg fixed point theorem and discuss the closedness of the strong solution set. Moreover, we also derive a stability result for this problem.

Existence results for systems of vector variational-like inequalities

The purpose of this paper is to introduce and study systems of vector variational-like inequalities in Banach spaces. Under certain conditions, some existence results for systems of vector variational-like inequalities in Banach spaces are obtained by Kakutani–Fan–Glicksberg fixed point theorem.

Fixed point theorems for compact multimaps on almost [formula omitted]-convex sets in generalized convex spaces

In this paper, we introduce the concept of the strict Kakutani multimap (KKM) property and investigate the fixed point problem for multimaps having this property on almost Γ -convex subsets of locally G -convex uniform spaces. Our new fixed point theorem generalizes the well-known Fan–Glicksberg fixed point theorem and partially extends the Himmelberg fixed point theorem. Its application to minimax theorem is also given.

New existence of equilibria in generalized SSC

The purpose of this paper is to prove new existence theorems of equilibria in generalized SSC without assuming the interior condition of the state correspondence nor the strong continuity assumption on agent's preference correspondence by using the Fan-Glicksberg fixed-point theorem, and also give some corollaries including the Nash equilibrium existence for an abstract economy. Our results generalize the corresponding results due to Keiding, Vind and Kim and Yuan in several ways.

Some applications of the Knaster-Kuratowski and Mazurkiewicz principle in hyperconvex metric spaces

In this paper, as applications of the Knaster-Kuratowski and Mazurkiewicz principle in the hyperconvex version, we obtain the Ky Fan type matching theorems for closed and open covers. As applications, some intersection theorems which are hyperconvex versions of corresponding results due to Alexandroff and Pasynkoff, Fan, Klee, Horváth, and Lassonde are established. Then, the Ky Fan type best approximation theorem and Schauder-Tychonoff fixed-point theorem (i.e., Fan-Glicksberg fixed-point theorem) for set-valued mappings in noncompact hyperconvex spaces are also given. Finally, we obtain a general form of the Browder-Fan fixed-point theorem for set-valued mappings in noncompact hyperconvex spaces. These results include corresponding results in the literature as special cases.

Coincidences and fixed points in locally G-convex spaces

A new coincidence point theorem is proved for a pair of multivalued mappings operating between G-convex spaces. From this theorem, a generalisation of the classical Fan-Glicksberg fixed point theorem is established.

Generalized minimax inequalities and fixed point theorems

Recently, many authors [1–3] have generalized the famous Ky Fan's minimax inequality. In this paper, we put forward T-diagonal convexity (concavity) conditions and develop the main results in this respect. Next, we discuss some fixed point problems, and generalize the Fan-Glicksberg's fixed point theorem [14].

Generalized bi-quasi-variational inequalities

Let E, F be Hausdorff topological vector spaces over the field Φ (which is either the real field or the complex field), let 〈 , 〉: F × E → Φ be a bilinear functional, and let X be a non-empty subset of E. Given a multi-valued map S: X → 2 x and two multi-valued maps M, T: X → 2 F , the generalized bi-quasi-variational inequality (GBQVI) problem is to find a point y ̂ ϵ X such that y ̂ ϵ S( y ̂ ) and inf w ϵ T( y ̄ ) Re〈ƒ − w, y ̂ − x〉 ⩽ 0 for all x ϵ S( y ̂ ) and for all ƒ ϵ M( y ̂ ) . In this paper two general existence theorems on solutions of GBQVIs are obtained which simultaneously unify, sharpen, and extend existence theorems for multi-valued versions of Hartman-Stampacchia variational inequalities proved by Browder and by Shih and Tan, variational inequalities due to Browder, existence theorems for generalized quasi-variational inequalities achieved by Shih and Tan, theorems for monotone operators obtained by Debrunner and Flor, Fan, and Browder, and the Fan-Glicksberg fixed-point theorem.