具有Fréchet可微范数的实一致凸Banach空间中可数严格伪压缩映射族的弱收敛定理  

Weak Convergence Theorems for a Countable Family of Strict Pseudocontraction Mappings in a Uniformly Convex Banach Space with the Fréchet Differentiable Norm

作　　者：王纯[1] 潘思明[1] 

机构地区：[1]成都信息工程学院数学学院,四川成都610225

出　　处：《成都信息工程学院学报》2011年第4期366-372,共7页Journal of Chengdu University of Information Technology

摘　　要：为了研究在具有Fréchet可微范数的实一致凸Banach空间中的可数的严格伪压缩映射族Mann型迭代方案的收敛性,利用Marino-Xu,Zhou,Osilike-Udomene,Zhang-Guo的结论以及其它相关的结论,在已有结论的基础上,将Chidume-Shahzad的某些结论推广到具有Fréchet可微范数的实一致凸Banach空间的无限严格伪压缩映射族的情形下,并给出了在具有Fréchet可微范数的实一致凸Banach空间中的可数严格伪压缩映射族的Mann型迭代方案弱收敛性的证明。In this paper,in order to investigate the convergences of Mann-type iterative scheme for a countable family of strict pseudocontraction mappings in a uniformly convex Banach space with the Fréchet differentiable norm,we used the results obtained by Marino-Xu,Zhou,Osilike-Udomene,Zhang-Guo and the corresponding results to extend some conclusions obtained by Chidume-Shahzad to the real uniformly convex Banach space with the Fréchet differentiable norm under the countable strictly pseudocontraction mappings.And the proof of the weak convergences of Mann-type iterative scheme for a countable family of strict pseudocontraction mappings in this Banach space with the Fréchet differentiable norm was given.

关 键 词：应用数学 非线性分析 公共不动点 收敛定理 λ-严格伪压缩映射 MANN迭代 一致凸BANACH空间 

分 类 号：O177.2[理学—数学]