Fan Minimax Inequality Research Articles

A TOPOLOGICAL MINIMAX INEQUALITY WITH <TEX>${\gamma}$</TEX>-DCQCV AND ITS APPLICATIONS

In this paper, using the <TEX>${\gamma}$</TEX>-diagonally <TEX>$\mathcal{C}$</TEX>-quasiconcave condition, we will prove a new minimax inequality in a non-convex subset of a topological space which generalizes Fan's minimax inequality and its generalizations in several aspects.

Existence theorems of generalized quasi-variational-like inequalities for η-h-pseudo-monotone type I operators on non-compact sets

In this article, we prove the existence results of solutions for a new class of generalized quasi-variational-like inequalities (GQVLI) for η-h-pseudo-monotone type I operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. In obtaining our results on GQVLI for η-h-pseudo-monotone type I operators, we use Chowdhury and Tan's generalized version of Ky Fan's minimax inequality as the main tool.

The existence of solutions for general variational inequality and applications in FC spaces

In this article, we prove the existence of solutions for the general variational inequality ϕ(x, y) ≥ f(x) - f(y) and Minty type theorem by using the generalized KKM theorem in topological spaces without linear structure. Some properties of solutions set for the general variational inequality are studied by Minty type theorem. As applications, equivalence between Browder fixed point theorem and Ky Fan's minimax inequality are studied in topological spaces.

Coincidence theorems and minimax inequalities in abstract convex spaces

Abstract In this paper, we deal with the notion of abstract convex spaces via minimal spaces as an extended version of other forms of convexity and establish some well-known results such as coincidence theorems for the classes m-KKM and ms-KKM of multimaps and Ky Fan's type minimax inequality. Mathematics Subject Classification (2000) 26A51; 26B25; 54H25; 55M20; 47H10; 54A05.

A minimax inequality and its applications to fixed point theorems in CAT(0) spaces

AbstractIn this paper, a CAT(0) version of famous Fan's minimax inequality is established and as its application, we obtain some fixed point theorems and best approximation theorems in CAT(0) spaces.2000 Mathematics Subject Classification: 47H10.

Generalized Bi-Quasivariational Inequalities for Quasi-Pseudomonotone Type II Operators on Noncompact Sets

We prove some existence results of solutions for a new class of generalized bi-quasivariational inequalities (GBQVI) for quasi-pseudomonotone type II and strongly quasi-pseudomonotone type II operators defined on noncompact sets in locally convex Hausdorff topological vector spaces. To obtain these results on GBQVI for quasi-pseudomonotone type II and strongly quasi-pseudomonotone type II operators, we use Chowdhury and Tan's generalized version (1996) of Ky Fan's minimax inequality (1972) as the main tool.

Stability of solutions for Ky Fan's section theorem with some applications

In this paper, we prove that “most of” problems in Ky Fan's section theorem (in the sense of Baire category) are essential and that for any problem in Ky Fan's section theorem, there exists at least one essential component of its solution set. As applications, we deduce both the existence of essential components of the set of Ky Fan's points based on Ky Fan's minimax inequality theorem and the existence of essential components of the set of Nash equilibrium points for general n-person non-cooperative games with non-concave payoffs.

Set-valued versions of Ky Fan's inequality with application to variational inclusion theory

In this paper, we prove two set-valued versions of Ky Fan's minimax inequality. From these results, versions of Schauder's and Kakutani's fixed point theorems can be deduced. We formulate a variational inclusion problem for set-valued maps and a differential inclusion problem, concerning the contingent derivative. Sufficient conditions for the existence of solution for these inclusion problems are obtained, generalizing classical variational inequality problems.

A Counterexample to 0-Diagonal Quasiconcavity in a Minimax Inequality

In this paper, a very simple example shows that, in a n- person nonzero-sum game, the quasiconvexity of the payoff functions is not sufficient to establish the 0-diagonal quasiconcavity in the Fan minimax inequality.

Existence theorems of generalized quasi-variational inequalities with upper hemi-continuous and demi operators on non-compact sets

Suppose that E is a topological vector space and X is a non-empty subset of E. Let S: X --> 2(X) and T:X --> 2(E)* be two maps. Then the generalized quasi-variational inequality problem (GQVI) is to find a point (y) over cap is an element of S((y) over cap) and a point (w) over cap is an element of T((y) over cap) such that Re[(w) over cap, (y) over cap - x] less than or equal to 0 far all x is an element of S((y) over cap). We shall use Chowdhury and Tan's generalized version [4] of Ky Fan's minimax inequality [7] as a tool to obtain some general theorems on solutions of the GQVI in locally convex Hausdorff topological vector spaces. We obtain the existence theorems of GQVI on paracompact sets X where the set-valued operators T are demi operators [3] and are upper hemi-continuous [5] along line segments in X to the weak * -topology on E*.

A New Generalization of Browder Fixed Point Theorem with Applications

Abstract In the present paper, a new generalization of Browder fixed point theorem is obtained. As its applications, we obtain some generalized versions of Browder's theorems for quasi-variational inequality and Ky Fan's minimax inequality and minimax principle.

Generalization of Ky Fan's Minimax Inequality with Applications to Generalized Variational Inequalities for Pseudo-Monotone Operators and Fixed Point Theorems

Generalization of Ky Fan's Minimax Inequality with Applications to Generalized Variational Inequalities for Pseudo-Monotone Operators and Fixed Point Theorems

On Fan's Minimax Inequality

We study Fan's minimax inequality miny∈Csupx∈Cf(x,y)≤supx∈Cf(x,x), under different assumptions onfandCin locally convex topological vector spaces. The main generalization is the weaking of “convex” to “acyclic.” The aim of this paper is to develop as consequence of several fixed point theorems and coincidence theorems a variety of existence results relevant to minimax inequalities. As an application, some variational inequalities are deduced without monotonicity nor coercivity.

Generalized KKM theorem and variational inequalities

The purpose of this paper is to introduce the concept of generalized KKM mapping and to obtain some general versions of the famous KKM theorem, Ky Fan's minimax inequality, and the Browder-Hartman-Stampacchia variational inequality theorem. As applications we utilize these results to study the saddle point problem and the existence problem of solutions for a class of quasi-variational inequalities. The results presented in this paper extend and improve some recent results of other authors.

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].

Some further generalizations of Ky Fan's minimax inequality and its applications to variational inequalities

The purpose of this paper is to introduce the concept of generalized KKM mapping and to obtain some general version of the famous KKM theorem and Ky Fan's minimax inequality. As applications, we utilize the results presented in this paper to study the saddle point problem and the existence problem of solutions for a class of quasi-variational inequalities. The results obtained in this paper extend and improve some recent results of [1–6].