Systems of Generalized Quasivariational Inclusion Problems with Applications in <inline-formula> <graphic file="1687-1812-2011-561573-i1.gif"/></inline-formula>-Spaces

Abstract

We first prove that the product of a family of -spaces is also an -space. Then, by using a Himmelberg type fixed point theorem in -spaces, we establish existence theorems of solutions for systems of generalized quasivariational inclusion problems, systems of variational equations, and systems of generalized quasiequilibrium problems in -spaces. Applications of the existence theorem of solutions for systems of generalized quasiequilibrium problems to optimization problems are given in -spaces.