Iterative Approximations Of Fixed Points In Banach Spaces

The problem of fixed points is one of the emphasis problems of people's regard and the corresponding research has gained many great achievements.Among many directions of the fixed point researches,it becomes main problem that the convergence problem about constructing approximating fixed point sequences and its application in control ,nonlinear operator and derivative equation etc.The research of this problem will play an important role in its application in reality.The purpose of this paper is to study some problems about iterative approximations of fixed points for L-Lipschitz mappings and the equivalence of iterative sequences convergence of fixed points.The paper consists of four parts.The main results of this paper are summarized as following:In the first chapter,we simply narrate the development of the fixed point theory home and abroad in the preface.And the main content that we will discuss,background and significance are introduced.In the second chapter,some definitions,lemmas and related knowledge used in the article are introduced in the preparation.In the third chapter,the main theorems about iterative approximations of fixed points for uniformly L-Lipschitz mappings in normed linear spaces,the sufficient and necessary conditions and the sufficient conditions on the convergence of the modified Ishikawa and Mann iterative sequence with errors for uniformly L–Lipschitz mappings in Banach spaces, the convergence of the modified three iterative sequences for uniformly L-Lipschitz mappings in Banach spaces and iterative approximations of fixed points for asymptotically nonexpansive mappings in Banach spaces are described and proved.In the last chapter,the equivalence theorems about iterative sequences convergence of fixed points are described and proved.