渐近拟伪压缩型映像不动点的迭代算法收敛性

发布时间：2018-01-01 11:03

本文关键词：渐近拟伪压缩型映像不动点的迭代算法收敛性　出处：《浙江师范大学》2016年硕士论文　论文类型：学位论文

【摘要】：在本文中,我们主要研究了两个结果.结果一,在一致光滑、严格凸、含有Kadec—Klee性质的实Banach空间E中给出了一种新的迭代格式,用于逼近一族依中间意义渐近严格拟φ-伪压缩映像不动点与广义均衡问题解的公共点,并在一定条件下证明该序列的强收敛性.这个新的广义混杂迭代序列{xn}定义如下：其中Ti是一致渐近严格拟φ-伪压缩映像；J是正规对偶映射；F是给定的函数；ΠfCn+1是广义f-投影算子.在一定条件下,证明该迭代序列{xn}强收敛到一族闭的依中间意义一致渐近严格拟φ一伪压缩型映像不动点与广义平衡问题解的公共点.相对于近代已有的结果,其结果主要从投影算子、迭代方式、均衡问题、空间范围、非线性映射这5个方面做了相应的推广和改进.结果二,设G是一般的实Banach空间上的收缩核,P是收缩映像,引入了带误差修正的I shikawa迭代序列{xn}：其中Hi,Kj是两个一致L-Lipschitzian非自映像族,Hi是一渐进拟伪压缩型映像族.当满足适当条件时,证明了该迭代序列{xn}强收敛于一族非自渐近拟伪压缩型映像的公共不动点.其结果在映射、迭代形式、证明方法上改进和推广了现代一些作者的相关成果.文章的结构是：第一章介绍了相关的研究背景、概念、引理；第二章证明了依中间意义一致渐近严格拟φ-伪压缩映像与广义平衡问题解的新的混杂迭代序列的强收敛性;第三章研究了关于两族非自渐近拟伪压缩型映像族公共不动点的修正的Ishikawa迭代序列的收敛性.
[Abstract]:In this paper, we mainly study two results. First, we give a new iterative scheme in the uniformly smooth, strictly convex, real Banach space E with Kadec-Klee property. It is used to approximate the fixed points of a family of asymptotically strictly quasi-蠁 -pseudocontractive mappings and the common points of solutions to generalized equilibrium problems. The new generalized hybrid iterative sequence {xn} is defined as follows: where Ti is uniformly asymptotically strictly quasi-蠁 -pseudocontractive mapping; J is a normal dual mapping; F is a given function; FCn 1 is a generalized f-projection operator under certain conditions. It is proved that the iterative sequence {xn} strongly converges to a family of closed fixed points for uniformly asymptotically strictly quasi-蠁 -pseudocontractive type mappings with intermediate meaning and common points for solutions of generalized equilibrium problems. The results are generalized and improved from five aspects: projection operator, iterative method, equilibrium problem, spatial range and nonlinear mapping. Let G be a contraction kernel P on a general real Banach space, and introduce the I shikawa iterative sequence {XN} with error correction: hi. KJ is two uniform L-Lipschitzian nonself-mappings. Phi is a class of asymptotically quasi-pseudocontractive mappings. It is proved that the iterative sequence {xn} strongly converges to a common fixed point of a class of nonself-asymptotically quasi-pseudo-contractive mappings. The results are in the form of mappings and iterations. The structure of this paper is as follows: the first chapter introduces the relevant research background, concepts and Lemma; In chapter 2, we prove the strong convergence of the new hybrid iterative sequences for uniformly asymptotically strictly quasi-蠁 -pseudocontractive mappings and generalized equilibrium problems. In chapter 3, we study the convergence of modified Ishikawa iterative sequences for two families of nonasymptotically quasi-pseudo-contractive mappings with common fixed points.
【学位授予单位】：浙江师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O177.91

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