【作者】 许炎；

【导师】 郭伟平；

【作者基本信息】 苏州科技学院 ， 基础数学， 2010， 硕士

【摘要】 不动点问题一直是人们关注的重点问题之一,有关这方面的研究也取得了显著的成绩。在不动点问题研究的众多方向中,关于构造渐近不动点序列的迭代收敛问题以及在控制、非线性算子和微分方程等方面的理论结合及应用成为研究的主流问题,对这方面问题的研究会在实际运用中起到至关重要的作用。本文主要研究了L-Lipschitz映射的不动点迭代逼近以及不动点迭代序列收敛的等价性问题。全文共分四部分:第一章绪论:简单阐述国内外有关不动点理论的发展概况,并介绍本文要讨论的主要内容、背景和意义。第二章预备知识:主要引入文中用到的一些定义、引理及相关知识。第三章L-Lipschitz映射的不动点迭代逼近:给出了赋范线性空间中一致L-Lipsc -hitz映射的不动点迭代逼近定理、Banach空间中一致L-Lipschitz映射的(带误差修改的)Ishikawa迭代序列和(带误差修改的)Mann迭代序列的不动点迭代逼近的充要条件和充分条件、修改的三重迭代序列的收敛性以及渐近非扩张映射的不动点迭代逼近等问题的定理。第四章Ishikawa迭代序列和Mann迭代序列收敛的等价性:给出了带误差的Ishikawa迭代序列和带误差的Mann迭代序列收敛性的等价定理。更多还原

【Abstract】 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.更多还原