Approximation Approaches To Zero Points Of Families Of M-Accretive Operators And Applications

The theory of variational inequalities is an important part of the theory of nonlinear functional analysis. The main work is to use some iterative algorithms to find approximate the common zero point of two classes of m-accretive operators, which also solve a certain variational inequality.This paper includes three chapters. Now we describe them one by one. In Chapter 1,we recall the simple history of the nonlinear operator theory and introduce the main work of this paper. In Chapter 2, we introduce general iterative algorithms for finding common solutions of a mixed equilibrium problem, a general system of variational inequalities, and a common zero point problem of two classes of m-accretive operators in a real Hilbert space, and derive their strong convergence. In Chapter 3, we study two new iterative algorithms for the convex combination of finitely many nonexpansive mappings and two classes of m-accretive operators in real Banach spaces, and also apply them to solves a certain variational inequality. The results presented in this paper improve, extend and develop some recent corresponding results in the literature.