关于巴拿赫空间中非膨胀映射的一类扩展的石川迭代序列（英文）  

Aclass of extended ishikawa iterative processes in Banachspaces for nonexpansive mappings

作　　者：程丛电[1] 关洪岩[1] 

机构地区：[1]沈阳师范大学数学与系统科学学院,沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2016年第2期201-205,共5页Journal of Shenyang Normal University:Natural Science Edition

基　　金：Project supported by Department of Education of Liaoning Province(L2010514)

摘　　要：关于巴拿赫空间中非膨胀映射的迭代序列是否收敛到该映射的不动点问题已有许多研究工作;2004年,徐洪坤建立了一种扩展的曼恩迭代序列,并用黏性逼近方法在一致光滑巴拿赫空间的框架下证明了其收敛到该映射的不动点;2007年,张石生推广与改进了徐洪坤的工作。基于以往有关工作,进一步探讨巴拿赫空间中非膨胀映射的迭代序列的收敛性与非膨胀映射的不动点问题。利用算子替换常数值与向量给出了一类扩展的石川迭代序列;基于对偶映射与变分不等式理论,采用黏性逼近方法,证明了该迭代序列的某种强收敛性及一个有关不动点定理。由于所建立的迭代序列概括了多种类型的曼恩和石川迭代序列,此项工作发展与推广了该领域的许多近期研究成果。The problem whether a iterative process of nonexpansive mapping T in real Banach Spaces converges to its fixed point（IPNMCFP）has be extensively studied.Particularly,in 2004,Xu H K constructed a kind of extended Mann iterative process for nonexpansive mapping T,and by the so called viscosity approximation methods,he proved that the iterative process converges strongly to a fixed point of Tunder the uniformly smooth Banach Spaces.In 2007,Zhang S S developed the work of Xu H K.This paper further studies the problem IPNMCFP.By replacing constants with operators,the Ishikawa iterative process is generalized as a class of extended Ishikowa iterative process.Under some conditions,the strong convergence of the iterative process is proved in the viscosity approximation methods,using the theory of duality mapping and variational inequality.And in a special case the iterative process converges strongly to a fixed point of Tis also proved.For the introduced iterative process involves many kinds of Mann and Ishikawa iterative processes,the main conclusion of the present work extends and generalizes some recent results of this research area.

关 键 词：非膨胀映射 序列 曼恩(Mann)迭代 石川(Ishikawa)迭代 不动点 

分 类 号：O177[理学—数学]