【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x₀∈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.更多还原

【Abstract】 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^kx_n+γ_nu_n,n≥1,where {α_n},{β_n},{γ_n}∈[0,1]andα_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.更多还原