Fan-KKM Theorem Research Articles

Existence of Solutions for Abstract Economic Equilibrium Problems and Algorithm

In this paper, we study a new kind of vector equilibrium problem and we proved the existence of solutions for this kind of equilibrium problem by using the section theorem and Fan KKM theorem. Then we generalize this kind of vector equilibrium problem to a more general case. Equilibrium problems with lower and upper bounds was an open problem proposed by Isac, Sehgal and Singh in 1999. J. Li, O. Chadli, Y. Chiang and J.C. Yao, Zhang Cong-jun derived some results of the equilibrium problems with lower and upper bounds under certain conditions. In this paper we derive more results of this open problem under certain conditions, constructs an iteration algorithm, and discuses the convergence of the algorithm.

GENERALIZED NONLINEAR MULTIVALUED MIXED QUASI-VARIATIONAL-LIKE INEQUALITIES

In this paper, we introduce a new class of generalized nonlinear multivalued mixed quasi-variational-like inequalities and prove the existence and uniqueness of solutions for the class of generalized nonlinear multivalued mixed quasi-variational-like inequalities in reflexive Banach spaces using Fan-KKM Theorem.

Existence of solutions for generalized implicit vector variational-like inequalities

In this paper, we introduce a new class of generalized implicit vector variational-like inequalities in Hausdorff topological vector spaces and Banach spaces which contain implicit vector equilibrium problems, implicit vector variational inequalities and implicit vector complementarity problems as special cases. We derive some new results by using the KKM–Fan theorem, under compact and noncompact assumptions on underlying convex sets.

An existence result for generalized vector equilibrium problems without pseudomonotonicity

In this work, we introduce and study a class of generalized vector equilibrium problems for multifunctions which includes a number of generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. By using the KKM–Fan theorem and Nadler’s result, we prove an existence theorem for solutions for this class of generalized vector equilibrium problems in Banach spaces. Applications to generalized vector variational-like inequalities are given.

Some Existence Results for Vector Quasivariational Inequalities Involving Multifunctions and Applications to Traffic Equilibrium Problems

Some existence results for vector quasivariational inequalities with multifunctions in Banach spaces are derived by employing the KKM-Fan theorem. In particular, we generalize a result by Lin, Yang and Yao, and avoid monotonicity assumptions. We also consider a new quasivariational inequality problem and propose notions of weak and strong equilibria while applying the results to traffic network problems.

Auxiliary principle and fuzzy variational-like inequalities

The purpose of this paper is to introduce the concept of fuzzy variational-like inequalities and to study the existence problem and the iterative approximation problem for solutions of certain kinds of fuzzy variational-like inequalities in Hilbert spaces. By using the general auxiliary principle technique, Ky Fan's KKM theorem, Nadler's fixed point theorem, and some new analytic techniques, some existence theorems and some iterative approximation schemes for solving this kind of fuzzy variational-like inequalities are established. The results presented in this paper are new and they generalize, improve, and unify a number of recent results.

On generalized vector quasivariational-like inequality problems

We introduce a class of generalized vector quasivariational-like inequality problems in Banach spaces. We derive some new existence results by using KKM-Fan theorem and an equivalent fixed point theorem. As an application of our results, we have obtained as special cases the existence results for vector quasi-equilibrium problems, generalized vector quasivariational inequality and vector quasi-optimization problems. The results of this paper generalize and unify the corresponding results of several authors and can be considered as a significant extension of the previously known results.

On the existence of solutions of variational inequalities in Banach spaces

In this paper, we study the existence of the solution of the variational inequality 〈 Tx− ξ, y− x〉⩾0 by applying the generalized projection operator π K :B ∗→B , where B is a Banach space with dual space B ∗ and by using the well-known FanKKM Theorem.

On implicit vector equilibrium problems

In this paper, we introduce and study a class of implicit vector equilibrium problems, which includes a number of (scalar) implicit equilibrium problems, implicit variational inequalities, and implicit complementarity problems as special cases. By using KKM-Fan theorem, we prove some new existence theorems of solutions for this kind of implicit vector equilibrium problems in Hausdorff topological vector spaces. Our results extend and unify some corresponding results of several authors.

Some Minimax Type Results Of Clarke's Generalized Directional Derivative And Point-Coderivative Of Multifunctions

In this paper, we will apply some results which are associated with the techniques of KKM mapping and Fan-KKM Theorem to prove a fixed point theorem and to reprove a theorem of variational inequalities (Theorem 2 [3]) which relates with Clarke"s generalized directional derivative.

Some Eigenvector Theorems Proved by a Fan–KKM Theorem

In this paper, we use the technique of KKM mapping and a Fan–KKM theorem to study the existence of eigenvectors for some mappings on normed linear spaces.