几类渐近拟伪压缩型映像不动点的迭代算法

发布时间：2018-01-09 23:16

本文关键词：几类渐近拟伪压缩型映像不动点的迭代算法　出处：《浙江师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：本篇论文主要在实Banach空间中,研究了渐近拟伪压缩型映像的带误差的修改的Ishikawa迭代序列强收敛性,有限族增生算子公共零点的粘性逼近法,以及渐近非扩张映像不动点的迭代算法.结果一,在任意实Banach空间中引入带误差的修改的Ishikawa迭代序列{xn}定义并证明了迭代序列{xn}强收敛到依中间意义渐近非扩张的渐近拟伪压缩型映像的不动点.结果二,在严格凸的,具有弱连续的对偶映像Jφ的自反的Banach空间中,利用增生算子的预解算子,引入以下新的粘性迭代序列证明了当满足适当条件时,迭代序列{xn}强收敛到有限族增生算子公共零点.结果三,在一致凸Banach空间中,引入以下新的关于渐近非扩张映像不动点的迭代算法证明当满足适当条件时,该序列{xn}强收敛于渐近非扩张映像T的不动点x*,且x*是以下变分不等式的解这些结果在一定程度上改进和推广了最近一些其他作者的相关成果.文章的结构是：第一章介绍了相关的研究背景,与本篇论文相关的概念,引理;第二章证明了带误差的修改的Ishikawa迭代序列强收敛性；第三章研究了有限族增生算子公共零点的粘性逼近法；第四章讨论了渐近非扩张映像不动点的迭代算法.
[Abstract]:In this paper, we study the strong convergence of modified Ishikawa iterative sequences with errors for asymptotically quasi-pseudo-contractive type mappings in real Banach spaces. A common 00:00 viscous approximation method for a finite family of accretive operators and an iterative algorithm for fixed points of asymptotically nonexpansive mappings. In this paper, we introduce a modified Ishikawa iterative sequence {xn} with errors in arbitrary real Banach spaces and prove that the iterative sequence {xn} strongly converges to asymptotically nonexpansive in the intermediate sense. Fixed points of pseudo contractive type mappings. Results 2. In a reflexive Banach space with a weakly continuous dual mapping J 蠁, the following new viscous iterative sequences are introduced by using the resolvent operator of the accretive operator. The iterative sequence {xn} strongly converges to the common 00:00 of a finite family of accretive operators. Result 3, in uniformly convex Banach spaces. The following new iterative algorithm for fixed point of asymptotically nonexpansive mappings is introduced to prove that the sequence {xn} strongly converges to the fixed point x * of asymptotically nonexpansive mappings T when the appropriate conditions are satisfied. And x* is the solution of the following variational inequalities. To some extent, these results improve and generalize the related results of other authors. The structure of this paper is as follows: the first chapter introduces the relevant research background. The concepts and Lemma related to this paper; In chapter 2, the strong convergence of modified Ishikawa iterative sequences with errors is proved. In chapter 3, the viscous approximation method of common 00:00 for finite family of accretive operators is studied. In chapter 4th, the iterative algorithm for fixed points of asymptotically nonexpansive mappings is discussed.
【学位授予单位】：浙江师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O177.91

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