Optimality Conditions for Solving Nonconvex Set-Valued Equilibrium Problems

Document Type : Original Article

Author
Somaye Jafari
Department of Mathematics, Faculty of Sciences, Arak University, Arak 38156-8-8349, Iran.
10.29252/maco.1.1.12
Abstract
In this paper, sufficient conditions ensuring the existence of solutions for set-valued equilibrium problems are obtained. The convexity assumption on the whole domain is not necessary and just the closure of a quasi-self-segment-dense subset of the domain is convex. Using a KKM theorem and a notion of Q-selected preserving $R_{-}^{*}$-intersection
($R_{-}^{*}$-inclusion) for set-valued mapping, the existence results are proved in real Hausdorff topological vector spaces. 

Keywords

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Mathematical Analysis and Convex Optimization
Volume 1, Issue 1
June 2020
Pages 119-128