关于渐近非扩张映射的Cesàro意义下的修正Ishikawa迭代(英文)  

Modified Ishikawa Iteration of Cesàro Means for Asymptotically Non-expansive Mappings

作　　者：裴永刚[1] 

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《应用数学》2014年第3期519-528,共10页Mathematica Applicata

基　　金：Supported by the National Science Foundation Grant of China(11171094);the Key Scientific and Technological Project of Henan Province(142102210058)

摘　　要：设E是一致凸Banach空间,且具有一致Gteaux可微范数,C是E的一个非空闭凸子集,T是渐近非扩张映射.对于任意x∈C,本文引入Cesàro意义上的修正Ishikawa迭代:x0=x∈C,yn=γnun+δnxn+(1-γn-δ)n+11∑j=0nTjxn,xn+1=μnvn+αnγf(xn)+βnxn+[(1-μn-βn)I-αnA]n+11∑j=0nTjyn,n≥0在适当的条件下证明此迭代序列的强(弱)收敛性.Let Cbe a nonempty closed convex subset of a uniformly convex Banach space Ewith a uniformly Gteauxdifferentiablenorm.Suppose that T∶C →Cis an asymptotically nonexpansive mapping.For an arbitrary initial value x ∈C,we introduce the modified Ishikawa iteration of its Cesàro means：x0 =x∈C arbitrarily chosen,yn=γnun＋δnxn＋（1-γn-δ）n＋11∑j=0nTjxn,xn＋1=μnvn＋αnγf（xn）＋βnxn＋[（1-μn-βn）I-αnA]n＋11∑j=0nTjyn,n≥0and prove its strong and weak convergence under some mild conditions.

关 键 词：渐近非扩张映射 不动点 迭代算法 强(弱)收敛性 BANACH空间 

分 类 号：O177.91[理学—数学]