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Existence result for equilibrium problems | ||
| Journal of New Researches in Mathematics | ||
| مقاله 11، دوره 8، شماره 36، آذر و دی 2022، صفحه 139-148 اصل مقاله (278.42 K) | ||
| نوع مقاله: research paper | ||
| نویسنده | ||
Fatemeh Lael 
| ||
| Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran. | ||
| چکیده | ||
| Abstract We establish new sufficient conditions which guarantee existence of solutions of equilibrium Problems: 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, complementarity problems, 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. | ||
| کلیدواژهها | ||
| Convexity؛ Equilibrium problem؛ KKM principle؛ Minimization problem؛ Monotonicity | ||
| مراجع | ||
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