机构地区: 广东工业大学应用数学学院
出 处: 《数学物理学报(A辑)》 2010年第4期1062-1070,共9页
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.