有限个渐进非扩张非自映象的强收敛定理  

Strong Convergence Theorem of a Finite Family of Nonexpansive Non-self Mappings

作　　者：傅秋平[1] 谷峰[1] 

机构地区：[1]杭州师范大学理学院,浙江杭州310036

出　　处：《杭州师范大学学报（自然科学版）》2008年第3期172-176,共5页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：浙江省自然科学基金资助(Y605191);浙江省教育厅科研项目资助(20051897)

摘　　要：设E是一致凸Banach空间,C是E的非空闭凸子集,而且C也是E的非扩张收缩核,设{Ti}i=1N:C→E是N个渐进拟非扩张非自映象,定义新的迭代序列{xn}.该文证明了,若F=∩i=1NF(Ti)≠Φ且存在某Tl(1≤l≤N)是半紧的,则迭代序列{xn}强收敛于{Ti}i=1N的公共不动点.该文结果也改进和推广了一些人的最新结果.Let E be a real uniformly convex Banach space and C be a nonempty closed convex subset of E which is also a nonexpansive retract of E. Let {Ti}Ni=1：C→E be N asymptotically quasi-nonexpansive non-self mappings. A new iterative N sequence {xn } is defined. The paper also proves that if F=∩Ni=1F（Ti）≠φ and let there exist an Tl , 1 ≤l≤ N, which issemi-compact, then the sequence {xn }converges strongly to some common fixed point of {Ti}Ni=1. The results presented in this paper also extend and improve some recent results.

关 键 词：隐迭代序列 强收敛 渐进拟非扩张非自映象 一致凸BANACH空间 公共不动点 

分 类 号：O177.91[理学—数学]