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.
出处
《应用数学》
CSCD
北大核心
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
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
Uniformly convex Banach space
Nonself asymptotically nonexpansivemapping
Strong convergence
Weak convergence ~ Common fixed point
