Banach空间上广义渐近拟非扩张型映象不动点的逼近  

Approximation of Fixed Points of Generalized Asymptotic Quasi-nonexpansive Type Mapping

作　　者：向长合[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）》2005年第4期6-9,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金项目(No.10471159)

摘　　要：引入一类比渐近拟非扩张型映象更加广泛的广义渐近拟非扩张型映象,并给出具混合误差的Ishikawa迭代序列强收敛于广义渐近拟非扩张型映象的一个不动点的充要条件:设E是一Banach空间,T:E→E是广义渐近拟非扩张型映象,其渐近系数kn满足∑∞n=1(kn-1)<∞;若T在F(T)中的点处一致连续,任取一点x0∈E,{xn}是由下式定义的具混合误差的Ishikawa迭代序列xn+1=(1-αn)xn+αnTnyn+un,yn=(1-βn)xn+βnTnxn+vn,n≥0,其中{αn}、{βn}是[0,1]中的两个数列且∑∞n=0αn收敛,{un}、{vn}是E中两个点列且{vn}有界同时∑∞n=0un收敛。则{xn}强收敛于T在E中一个不动点的充要条件是lim infD(xn,F(T))=0。This paper introduces a generalized asymptotically quasi-nonexpansive type mapping-α class of mapping, which is more general than asymptotic quasi-nonexpansive type mapping and gives some necessary and sufficient conditions for the Ishikawa iterative sequence with mixed errors to converge strongly to a fixed point of generalized asymptotic quasi-nonexpansive type mapping. The results presented in this paper improve and generalize some recent results.

关 键 词：BANACH空间 渐近非扩张映象 渐近拟非扩张映象 渐近拟非扩张型映象 迭代序列 不动点 混合误差 

分 类 号：O177.91[理学—数学]