非线性算子具误差的隐迭代程序的强收敛性

Abstract

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^k x_n+γ_nu_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.

Key words: Total asymptotically nonexpansive mappings, Implicit iterative sequence with errors, Common fixed point, Uniformly convex Banach spaces, Demi-compact

CLC Number:

47H09

YANG Li-Ping, XIE Xiang-Sheng. Strong Convergence of Implicit Iterative Scheme with Errors for Nonlinear Mappings[J].Acta mathematica scientia,Series A, 2010, 30(4): 1062-1070.

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Strong Convergence of Implicit Iterative Scheme with Errors for Nonlinear Mappings

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