The Gap Functions And The Error Bounds Of Solutions And Related Algorithms Of A Class Of Set-valued Mixed Variational Inequalities

During the past ten years, since the variational inequality problem has been widelyapplied in the area of mathematics, physics, economics and other fields, thevariational inequality theory becomes an important branch in the study of thenonlinear analysis, which attracts the attention and interest of many scholars.On the basic of many previous research, we study the gap functions, the errorbounds of solutions and related algorithms of a class of set-valued mixed variationalinequalities. we also analyze the error bounds of solutions, establish thecorresponding generalized resolvent equations and prove the equivalence between thatclass of variational inequalities and the generalized resolvent equations.In this paper, we give three iterative algorithms of solving that class of set-valuedmixed variational inequalities and analyze the convergence of algorithms.This paper is divided into three chapters:In the first chapter, we introduce the background about the variational inequalitytheory in domestic and abroad, related ways and iterative algorithms of solving thevariational inequality problem.In the second chapter, we generalize a class of generalized mixed variationalinequalities and establish the gap functions and D-gap functions of the variationalinequality which we study, and we also analyze the error bounds of solutions.In the third chapter, we introduce the resolvent operator and establish thegeneralized resolvent equations about the variational inequality that we study, andprove the equivalence between generalized resolvent equations and that class ofvariational inequality, we also give three iterative algorithms of solving that class ofset-valued mixed variational inequalities and prove the convergence of algorithms bymaking good use of the resolvent operator technique.