General Iteration Metheds For Common Fixed Points Of Families Of Nonlinear Mappings

The theory of variational inequalities is an important part of the nonlinear functional analysis. The main work is to introduce some iterative algorithms for finding common fixed points of families of nonlinear operators, and also apply them to solve a certain variational inequality.This paper consists of three chapters. Now we describe them one by one. In Chapter1, we recall the simple history of the nonlinear operator theory and state the main work of this paper. In Chapter 2, we introduce two iterative algorithms for finding common fixed points of two families of nonexpansive mappings in a real Hilbert space, and derive their weak convergence. In Chapter 3, we study the Mann iteration process for finding a common fixed point of a finite family of strictly pseudocontractive mappings in a real q-uniformly smooth Banach space, derive its strong convergence, and also use it to solve a certain variational inequality. The results presented in this paper improve, extend and develop some recent corresponding results in the literature.