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Acta Mathematica Vietnamica

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

LE ANH TUAN, PHAM HUU SACH

Abstract

This paper gives existence theorems for solutions of the problem of finding a point (z0,x0,y0)B(z0,x0)×A(x0)×F(z0,x0,x0) such that, for all xA(x0),F(z0,x0,x)y0C(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.