Banach空间中可数拟-φ-渐近非扩张映像族的收敛定理  

Convergence Theorems for a Countable Infinte Family of Quasi-φ-asymptotically Nonexpansive Mappings in Banach Space

作　　者：陈进作[1] 吴定平[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》2013年第1期67-71,共5页Journal of Chengdu University of Information Technology

基　　金：国家自然科学基金资助项目(11171046);成都信息工程学院科研项目(KYTZ201004)资助

摘　　要：为了在光滑的严格凸的自反Banach空间中引入一类关于拟-φ-渐近非扩张映像族的混合迭代算法,并修正正规的Mann迭代算法以达到引入这种混合迭代算法强收敛的目的.采用Banach空间中的广义投影方法,使拟-φ-渐近非扩张映像族每次迭代生成的序列都投影在一个闭凸集合中,利用Lyapunov泛函和Banach空间中的K-K性质,证明了该序列收敛于其公共不动点,即在一定条件下得到了该混合迭代算法的强收敛性.所得结论是周海云和马丙坤等人的相关结果的改进与推广.The purpose of this article is to introduce a hybrid iteration algorithm relative to a class of quasi-φ-asymp- totically nonexpansive mappings and modify the normal Mann＇s iterative algorithm to have the strong convergence for this hybrid iteration algorithm. The sequence of quasi-J-asymptotically nonexpansive mappings generated by iteration is located in a closed and convex set by using the generalized projection in Banach space and then this sequence con- verges to a common fixed point is proved and study the strong convergence of this hybrid iteration algorithm under certain conditions. Its result hold in smooth, strictly convex, reflexive Banach spaces with K-K property and Lya- punov functional. The result of this paper improve and extend the corresponding ones announced by Zhou and Ma and others.

关 键 词：基础数学 泛函分析 拟-φ-渐近非扩张映像 广义投影 强收敛 混合迭代算法 公共不动点 

分 类 号：O143[理学—数学]