Convergence Of Iterative Sequences For Two Classes Of Nonlinear Oporators

The fixed point theory of nonlinear operators, as an important part of nonlinear function analysis, has been closely connected with many branches of modern mathematics and plays an important part for solving problems in these branches. Among many directions of the fixed point researches, it has become the mainstream to realize the application of convergence iterative sequences and various nonlinear operators on optimization, control and derivative equation, etc.This thesis, studying the problem on approximating to the fixed points of nonlinear operators, mainly contains three parts as following:In first part we introduce the background of nonlinear operator theory and the development of iterative methods, both of which lead the later parts of the thesis to a right direction.In second part we study the convergence of modified Ishikawa and Mann iterative sequence with random errors for p-almost asymptotically nonexpansive type of mapping. In uniformly convex Banach spaces, under the condition when Mapping is uniformly asymptotic regular and uniformly continuous, we apply viscosity approximation methods to obtain the convergence of modified Ishikawa and Mann iterative sequences with random errors when the sequence of positive numbers satisfies appropriate conditions.In third part we bring in a generalized p-asymptotically quasi-nonexpansive type of mapping, gives some necessary and sufficient conditions for the modified Ishikawa iterative sequences with mixed errors to converge strongly to a fixed point of generalized p-asymptotically quasi-nonexpansive type of mapping, and with the application of viscosity approximation methods in uniformly convex Banach spaces, the strong convergence theory of two iterative methods of the generalized p-asymptotically quasi-non-expansive type of mapping are obtained. Our results extend and improve the corresponding results of Chang S S, Feng and Xiang.