非线性算子具误差的隐迭代程序的强收敛性

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.

Strong Convergence of Implicit Iterative Scheme with Errors for Nonlinear Mappings

Let K be a nonempty closed convex subset of a real uniformly convex Banach space E and T_i: K → K~ (i=1, 2, …, N) be a finite family of total asymptotically nonexpansive mappings. Let the implicit iteration scheme {x_n} generated from arbitrary x₀∈K by x_n=α_nx_n-1+β_nT_n^k x_n+γ_n u_n, n≥1, where {α_n}, {β_n}, {γ_n} (  [0, 1] and α_n+β_n+γ_n=1, {u_n} is bounded in K. The purpose of this paper is to study several strong convergence of the implicit iteration scheme {x_n} 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.