Study On Problems Of Br Owder Variational Inequalities And Variational Inclusions

In this paper, we study Browder set-valued variational inequalitiesin real reflexive Banach spaces, and we discuss an existence theorem of solutions by using penalty technique. Our results improve and generalize many known results. By using the technique of the resolvent operator and Yosida approximant of monotone mappings and topological degree methods in real reflexive Banach spaces, we discuss an existence theorem of solutions for Browder set-valued variational inclusions, improve and extend the corresponding results of [6,7,8,9,13]. Finally, we suggest an iterative algorithm for finding the approximate solution of this class of inclusions in a uniformly convex and uniformly smooth Banach space.This thesis is divided into five sections. The first section is an introduction. The second section is preliminaries. In section three, we discuss generalized Browder set-valued variational inequalities in real reflexive Banach spaces. In section four, we discuss an existence theorem of solutions for a class of Browder set-valued variational inclusions. In section five, we discuss the convergence of Ishikawa iteration process in a uniformly convex and uniformly smooth Banach space. Our results generalize some results in [27].