Remarks on implicit vector variational inequalities.
In this paper, the authors consider two implicit vector variational inequalities. One is proposed and studied by the authors in [J. Optimization Theory Appl. 104, 409--425 (2000; Zbl 0970.47052)] and the other one is the generalized form of the previous one. They generalize the concepts of pseudomonotonicity and hemicontinuity which are earlier studied in [loc. cit]. By adopting the technique developed there the existence of solutions of these two implicit vector variational inequalities is studied. The strong solutions of these two inequalities are also studied by using the scalarization method of \textit{I.V. Konnov} and \textit{J. C. Yao} [J. Math. Anal. Appl. 206, 42-58 (1997; Zbl 0878.49006)] and by using a continuous selection theorem.
scientific article; zbMATH DE number 1876791