广义渐近拟非扩张型映象不动点的逼近  

Approximation of Fixed Points of a Generalized Asymptotically Quasi-nonexpansive Type Mapping

作　　者：胡国英[1] 梁天娟[1] 

机构地区：[1]重庆师范大学数学与计算机科学学院,重庆400047

出　　处：《重庆师范大学学报（自然科学版）》2008年第1期10-13,共4页Journal of Chongqing Normal University:Natural Science

基　　金：重庆市教委项目(No.KJ070806)

摘　　要：本文讨论了Banach空间中非空闭凸子集上的广义渐近拟非扩张型映象的迭代逼近问题,给出了具误差的修改的Ishikawa迭代序列{xn}强收敛到广义渐近拟非扩张型映象T不动点的充要条件:设E是Banach空间,C是E中的非空闭凸子集,T∶C→C是广义渐近拟非扩张型映象,其渐近系数kn满足∑∞n=1(kn-1)<∞,又设F(T)有界,且T在F(T)中的点处一致连续。任取一点x0∈C,{xn}是根据xn+1=αnxn+βnTnyn+γnunyn=ξnxn+ηnTnxn+δnvn定义的具误差的修改的Ishikawa迭代得到的,其中{un},{vn}是C中的两个有界点列,{αn},{βn},{γn},{ξn},{ηn},{δn}是[0,1]中的6个数列且满足αn+βn+γn=1,ξn+ηn+δn=1,∑∞n=1βn<+∞,∑∞n=1γn<+∞。则{xn}强收敛于T的不动点的充要条件是limn→∞infd(xn,F(T))=0,其中d(x,A)为x到集合A的距离。本文的结果推广改进了文献[1-7]中的结论。The purpose of this paper is to study the strong convergence of a generalized asymptotically quasi-nonexpansive type mapping in the non-empty closed and convex subset in Banach spaces,and to give some necessary and sufficient conditions for the modified Ishikawa iterative sequence with errors to converge strongly to a fixed point of the generalized asymptotically quasi-nonexpansive type mapping.Let E is a Banach space,C is a nonempty closed convex subset of E,and T∶C→C is a generalized asymptotically quasi-nonex-pansive type mapping with asymptotically Coefficient k. such that ∑∞n=1（kn-1）〈∞,Let F（T） is bounded,and T stongly converges to a point of F（T） again. Define the modified Ishikawa iterative sequence{x}with error as given in （ 1 ） with{Un},{Un}bounded sequences in C and {αn},{βn},{γn},{ξn},{ηn},{δn}sequences in {0,1}satisfying αn＋βn＋γn=1,ξn＋ηn＋δn=1,∑∞n=1βn〈＋∞,∑∞n=1γn〈＋∞,Then,{Xn}converges to a fixed point of T. If and only if lim inf d（Xn,F（T））=0where d（x,A） denotes the distance of x to set A. The results presented in this paper extend and improve the corresponding results of refs[ 1-7 ].

关 键 词：非空闭凸集 广义渐近拟非扩张型映象 ISHIKAWA迭代 不动点 

分 类 号：O177.91[理学—数学]