一致正规结构与Reich的公开问题的解答  

Uniform Normal Structure and Solutions of Reich's Open Question

作　　者：曾六川[1] 

机构地区：[1]上海师范大学数学系,上海200234

出　　处：《应用数学和力学》2005年第9期1097-1104,共8页Applied Mathematics and Mechanics

基　　金：高等学校优秀青年教师教学和科研奖励基金资助项目;上海市曙光计划基金资助项目

摘　　要：在具有一致正规结构且其范数是一致Gateaux可微的Banach空间中,研究了Reich提出的公开问题.在给渐近非扩张映象作更适当的假设下,对Reich的公开问题给出了一个肯定的答复.所得结果在下列方面推广与改进了张石生教授的最新结果:(ⅰ)去掉了张教授的较强条件“迭代参数列收敛到零”;(ⅱ)去掉了张教授的较强假设“渐近非扩张映象有不动点”;(ⅲ)也去掉了张教授的较强条件“Banach压缩映象原理生成的序列强收敛”.而且,这些结果也推广与改进了先前由Reich,Shioji,Takahashi,Ueda及Wittmann等多位作者得到的相应结果.The open question raised by Reich is studied in a Banach space with uniform normal structure, whose norm is uniformfly Gateaux differentiable. Under more suitable assumptions imposed on an asymptotically nonexpansive mapping, an affirmative answer to Reich＇s open question is given. The results presented extend and improve ZHANG Shi-sheng＇s recent ones in the following aspects： （i） ZHANG＇s stronger condition that the sequence of iterative parameters converges to zero is removed; （ ii ） ZHANG＇s stronger assumption that the asymptotically nonexpansive mapping has a fixed point is removed; （ iii ） ZHANG＇s stronger condition that the sequence generated by the Banach Contraction Principle is strongly convergent is also removed. Moreover, these also extend and improve the corresponding ones obtained previously by several authors including Reich, Shioji, Takahashi, Ueda and Wittmann.

关 键 词：渐近非扩张映象 不动点 一致正规结构 一致Gateaux可微范数 迭代逼近 

分 类 号：O177.91[理学—数学]