Volume 1, Issue 1 (6-2020)
MACO 2020, 1(1): 119-128 |
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Abstract: (1731 Views)
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.
($R_{-}^{*}$-inclusion) for set-valued mapping, the existence results are proved in real Hausdorff topological vector spaces.
Keywords: Set-valued equilibrium problem, Quasi-self-segment-dense set, Quasiconvexity, Generalized semicontinuity, Topological vector space.
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