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The solution sets and connectedness for weak vector variational inequalities. (Chinese. English summary) Zbl 1199.58010

Summary: The existence and connectedness of solutions for weak vector variational inequalities and their scalarization with a \(C\)-monotone mapping from a topological vector space to continuous linear mapping space \(L(X, Y)\) are shown. With the \(C\)-weak hemicontinuity and \(C\)-monotonicity for a mapping, and set-valued mapping fixed point theorems, the connectedness is derived by discussing the properties of set-valued mapping induced by solution sets of a scalarization variational inequality related to weak vector variational inequalities.

MSC:

58E35 Variational inequalities (global problems) in infinite-dimensional spaces
49J27 Existence theories for problems in abstract spaces
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