Huang, Longguang The solution sets and connectedness for weak vector variational inequalities. (Chinese. English summary) Zbl 1199.58010 Acta Math. Sci., Ser. A, Chin. Ed. 29, No. 1, 114-120 (2009). 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 Keywords:weak vector variational inequalities; scalarization vector variational inequalities; dual cone; \(C\)-weak hemicontinuous; \(C\)-monotone PDFBibTeX XMLCite \textit{L. Huang}, Acta Math. Sci., Ser. A, Chin. Ed. 29, No. 1, 114--120 (2009; Zbl 1199.58010)