Closedness of the solution map for parametric vector equilibrium problems with trifunctions (Q2891130)

New definitions of vector topological pseudomonotonicity are introduced. Using this new concept the author studies generalized parametric vector equilibrium problems with trifunctions on \(K\times D\times K\) into a real topological vector space \(Z\) with an ordering cone \(C\). Let \(X,\;Y,\;P\) be Hausdorff topological spaces and elements of \(P\) are parameters. Let \(T:X\to 2^Y\) be a multi-valued mapping. Let \(f_p:X\times Y\times X\to Z\) be a trifunction. Generalized vector equilibrium problem is formulated as follows:NEWLINENEWLINE \noindent For a given \(p\in P\) find a pair \((x_p,y_p)\in K_p\times T(x_p)\) such that NEWLINE\[NEWLINEf_p(x_p,y_p,u)\in (-IntC)^c ~~ \forall u\in K_p,NEWLINE\]NEWLINE where \((-IntC)^c=Z\setminus (-Int C)\) and \(K_p\) is a nonempty subset of \(X\).NEWLINENEWLINE Conditions for the closedness of the solution map defined on \(P\) are derived and the Hadamard well-posedness of the generalized parameter vector equilibrium problems is investigated.