（Lα）一致李普希兹渐进非扩张映射的迭代问题论文.doc

摘  要  　 摘　　　　　　要　 　 　　　　近年来 学者们对迭代序列收敛性的研究可谓层出不穷 Tan 和 Xu［１］已经 证明了建立在一致凸 Banach 空间紧凸子集上的渐进非扩张映射的 Ishikawa 迭代 序列的收敛原理 随之 刘齐侯［３］又阐述了 Banach 空间上渐进准非扩张映射 T  的具误差的 Ishikawa 迭代序列收敛于 T 的不动点的充分必要条件  之后  Xu 和  Noor［５］也证明了定义在一致凸 Banach 空间某非空有界闭凸子集上的渐进非扩 张映射的三步迭代序列的收敛原理 从中得到启发 在本文我们首先定义了一致  凸 Banach 空间某非空紧子集上的一种新的映射－－－ L －??  一致李普希兹渐进 非扩张映射 在该紧子集上构造关于 L －?? 一致李普希兹渐进非扩张映射的 三步迭代序列以及具误差的三步迭代序列 先来讨论三步迭代序列的收敛性 进  而讨论具误差的三步迭代序列的收敛性 　  　  　 关键词 不动点 三步迭代 渐进非扩张映射 渐进准非扩张映射 紧子集 　 L －??  一致李普希兹 一致凸 Banach 空间  具误差的三步迭代  　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 I Abstract 　 Abstract In recent years , The convergence of iteration processes has been studied extensively by many authors . Tan and Xu [1] had proved the theorem on convergence  of  Ishikawa iteration processes of asymptotically nonexpansive mapping on a  compact convex subset of a uniform convex Banach space , Then Liu Qihou [3] presents the necessary and sufficient conditions for the Ishikawa iteration of asymptotically quasi-nonexpansive mapping with an error member on a Banach space convergent to a fixed point . Xu and Noor [5] had proved the theorem on convergence of three-step iterations of asymptotically nonexpansive mapping on nonempty closed , bounded and convex subset of uniformly convex Banach space . Inspired by these results , in this paper , we first give the definition of a new mapping ---?? L?????? uniformly Lipschitz asymptotically nonexpansive mapping on a compact subset of a uniform convex Banach space , then construct three-step iterative  sequences of ? L??????  uniformly Lipschitz asymptotically nonexpansive mapping in  this subset . We proved the convergence of this three-step iterative sequences for ? L??????  uniformly Lipschitz asymptotically nonexpansive mapping , Further more,  we proved this three-step iterative sequences with an error member converge to fixed points.  Key words: Fixed point ;  Three-step iterations ; Asymptotically nonexpansive  mapping ; Asymptotic