The generalized vector quasi-variational-like inequalities

In this paper, we introduce and study a class of Generalized Vector Quasi-V ariational-Like Inequality Problem (GVQVLIP) involving set-valued mappings with certain monotonicity. By employing the scalarization technique, severa l existence results for solutions of the (GVQVLIP) are established under no ncompact setting in topological vector spaces. These new existence results improve, unify, and generalize many known results for scalar and vector var iational inequalities in recent literature. (C) 1999 Elsevier Science Ltd. All rights reserved.