自反Banach空间中严格伪压缩映射可数族的弱收敛定理  

Weak Convergence Theorems for a Countable Family of Strict Pseudocontractions in Real Reflexive Banach Spaces

作　　者：潘思明[1] 王纯[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373-378,共6页Journal of Chengdu University of Information Technology

摘　　要：为了研究在具有Opial’s条件的实Fréchet光滑自反Banach空间中严格伪压缩映射可数族Mann型迭代序列的收敛性,利用Daruni Boonchari,Satit Saejung的结论以及其它相关的结论,在已有结论的基础上,将DaruniBoonchari,Satit Saejung的某些结论推广到具有Opial’s条件的实Fréchet光滑自反Banach空间的情形,并给出了在具有Opial’s条件的实Fréchet光滑自反Banach空间中的可数严格伪压缩映射族的Mann型迭代序列弱收敛性的证明。In this paper,in order to investigate the convergences of Mann-type iterative scheme for a countable family of strict pseudocontraction mappings in a real reflexive Banach space with the Fréchet differentiable norm,we used the results obtained by Daruni Boonchari,Satit Saejung and the corresponding results,and some conclusions obtained by Daruni Boonchari,Satit Saejung are extended and improved to the real reflexive Banach space with the Fréchet differentiable norm,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 is given.

关 键 词：应用数学 非线性分析 公共不动点 Opial’s条件 λ-严格伪压缩映射 MANN迭代 Fréchet光滑自反Banach空间 

分 类 号：O177.2[理学—数学]