非线性算子具误差的隐迭代程序的强收敛性  

Strong Convergence of Implicit Iterative Scheme with Errors for Nonlinear Mappings

作　　者：杨理平[1] 谢湘生[2] 

机构地区：[1]广东工业大学应用数学学院,广州510090 [2]广东工业大学系统工程研究所,广州510090

出　　处：《数学物理学报（A辑）》2010年第4期1062-1070,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(70871028;70671029)资助

摘　　要：设K是一致凸Banach空间中的非空闭凸子集,T_i:K→K(i=1,2,…,N)是有限族完全渐近非扩张映象.对任意的x_0∈K,具误差的隐迭代序列{x_n}为:x_n=α_nx_n-1+β_nT_n^kx_n+γ_nu_n,n≥1,其中{α_n},{β_n},{γ_n}■[0,1]满足α_n+β_n+γ_n=1,{u_n}是K中的有界序列.在一定的条件下,该文建立了隐迭代序列{x_n}的强收敛性.得到隐迭代序列{x_n}强收敛于有限族完全渐近非扩张映象公共不动点的充要条件.所得结果改进和推广了Shahzad与Zegeye,Zhou与Chang,Chang,Tan,Lee与Chan等人的相应结果.Let/（ be a nonempty closed convex subset of a real uniformly convex Banach space E and Ti：K→K（i=1,2,…,N） be a finite family of total asymptotically nonexpansive mappings. Let the implicit iteration scheme （xn} generated from arbitrary x_0∈K by xn=αnx_n-1＋β_nT_n^kx_n＋γ_nu_n,n≥1,, where （αn）, {βn}, {γn} [0, 1] and αn ＋βn ＋γn = 1, {un} is bounded in K. The purpose of this paper is to study several strong convergence of the implicit iteration scheme {xn} under certain conditions. It derives a necessary and sufficient condition for the strong convergence of this iteration scheme to a common fixed point of these mappings. The results of this paper improve and extend the corresponding results of Shahzad and Zegeye, Zhou and Chang, Chang, Tan, Lee and Chan.

关 键 词：完全渐近非扩张映象 具误差的隐迭代序列 公共不动点 一致凸BANACH空间 半紧 

分 类 号：O177.91[理学—数学]