Existence result for equilibrium problems

Subject Areas : Statistics

Fatemeh Lael ¹

1 - Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran.

Received: 2020-12-06 Accepted : 2021-03-05 Published : 2022-06-22

Keywords: اصل KKM, مسئله تعادل, تحدب, مسئله مینیمم, یکنوایی,

Abstract :

AbstractWe establish new sufficient conditions which guarantee existence of solutions of equilibriumProblems:Let K be a nonempty subset of a topological space E and f . The problem of interest, called equilibrium problem, is defined as follows:Find x such that f(x,y)>0 for all y: This problem is very general in the sense that it includes, as special cases, complementarityproblems, fixed point problems, minimax problems, Nash equilibrium problem in non-cooperative games, optimization problems and variational inequality problems, to name a few. As a matter of fact, this formulation unifies these problems in a convenient way, and many of the results obtained.Our results are without making any convexity and monotonicity assumptions on the underlying problem data. Our results are based upon the relation between the KKM principle and equilibrium problems through constructing a certain family of subsets of a given Hausdorff topological vector space. We also illustrate our developments and describe applications by adapting our existence results for non-convex minimization problems.

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