渐近非扩张非自映射的收敛定理(英文)  

Convergence Theorems for Nonself Asymptotically Nonexpansive Mappings

作　　者：阚绪周[1] 郭伟平[1] 

机构地区：[1]苏州科技学院数理学院,江苏苏州215009

出　　处：《应用数学》2012年第3期638-647,共10页Mathematica Applicata

基　　金：Supported by the Foundation for Major Subject of Suzhou University of Science and Technology

摘　　要：设E是实的一致凸Banach空间，K是E的一个非空闭凸集，P是E到K上的非扩张的保核收缩映射．（i）如果T1，T2，T3中有一个是全连续的或者半紧的，则{xn）强收敛于某一点q∈F；（ii）如果E具有Frechet可微范数或者满足Opial＇s条件或者E的对偶空间E＊具有Kadec—Klee性质，则{xn）弱收敛于某一点q∈F．Suppose that K is a nonempty closed convex subset of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T1, T2, T3 ： K→ E be three nonself asymptotically nonexpansive mappings with sequences where {an }, {βn} and {γn} are three real sequences in [-ε, 1- ε] for some e 〉 0. （i） If one of T1, T2 and T3 is completely continuous or demicompact,then strong convergence of {xn } to some q E F are obtained. （ii） If E has a Fr6chet differentiable norm or satisfying Opial＇s condition or its dual E has the Kadec-Klee property,then weak convergence of {xn } to some q E F are obtained.

关 键 词：一致凸BANACH空间 渐近非扩张非自映射 强收敛 弱收敛 公共不动点 

分 类 号：O177.91[理学—数学]