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An existence result for the generalized vector equilibrium problem. (English) Zbl 1014.49008
Let $$X$$ and $$Y$$ be two topological vector spaces, $$K$$ a nonempty convex subset of $$X$$, and $$F : K \times K \to 2^Y$$ a multifunction. Let $$C : K\to 2^Y$$ be a multifunction such that for each $$x\in K$$, $$C(x)$$ is a closed convex cone with $$\text{int }C(x)\neq 0$$, where $$\text{int } C(x)$$ denotes the interior of $$C(x)$$. Then, the authors consider the following generalized vector equilibrium problem which consists of finding $F(\overline x, y)\nsubseteq -\text{int }C(\overline x)\quad \text{for all } y\in K.$ By using the Fan-Browder type fixed-point theorem due to E. Tarafdar [J. Math. Anal. Appl. 128, 475-479 (1987; Zbl 0644.47050)], they present an existence result for the above problem, extending the result in E. Tarafdar and G. X.-Z. Yuan [Nonlinear Anal., Theory Methods Appl. 30, No. 7, 4171-4181 (1997; Zbl 0912.49004)]. It is very interesting for us.
Reviewer: Kim Jong-Kyu

##### MSC:
 49J40 Variational inequalities 47H10 Fixed-point theorems 49J53 Set-valued and variational analysis
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##### References:
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