EXISTENCE OF SOLUTIONS OF GENERALIZED QUASIVARIATIONAL INEQUALITIES WITH SET-VALUED MAPS

Le Anh Tuan and Pham Huu Sach

Abstract

                   This paper gives existence theorems for solutions of the problem of  finding a point (z₀ , x₀ , y₀)∈ B(z₀ , x₀) x A(x₀) x F((z₀ , x₀ , x₀)) such that, for all x∈ A(x₀), F((z₀ , x₀ , x) - y₀ ¢ C(z₀ , x₀ , x₀), where A,B,C and F are set-valued maps between topological vector spaces. Our results generalize some known existence theorems for quasivariational inequalities.