带误差的合成隐迭代新算法

Abstract

Abstract:

In this paper, a new composite implicit iterative process with errors for a family of asymptotically nonexpansive mappings was reasonably introduced in view of Banach's contraction principle, and a new theorem for weak and strong convergence was obtained under some suitable conditions, which deduced a new convergent theorem for a non-implicit iterative process with errors. It is worthy to say that this result extend the corresponding results of S.S.Chang [1] from implicit iterative process to non-implicit algorithm without any additive assumptions.

Key words: Uniform , convexity, Asymptotically nonexpensive mappings, Common fixed point

CLC Number:

47H09

RAO Ro-Feng. New Composite Implicit Iterative Scheme With Errors[J].Acta mathematica scientia,Series A, 2009, 29(3): 823-831.

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References

[1] Chang S S. On the convergence of implicit iterative process with error for a finite family of asymptotically nonexpansive mappings. J Math Anal Appl, 2006, 313: 273--283

[2] Bauschke H H. The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space. J Math Anal Appl, 1996, 202: 150--159

[3] Halpern B. Fixed points of nonexpansive mappings, Bull Amer Math Soc, 1967, 73: 957--961

[4] Lions P L. Approximation de points fixes de contractions. C R Acad Sci Paris Ser A, 1977, 284: 1357--1359

[5] Gornicki J. Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces. Comment Math Univ Carolin, 1989, 301: 249--252

[6] Wittmann R. Approximation of fixed points of nonexpansive mappings. Arch Math, 1992, 58: 486--491

[7] Xu H K, Ori M G. An implicit iterative process for nonexpansive mappings. Numer Funct Anal Optim, 2001, 22: 767--773

[8] Zhou Y Y, Chang S S. Convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings in Banach spaces. Numer Funct Anal Optim, 2002, 23: 911--921

[9] Chang S S, Cho Y J, Zhou H Y. Demi-closed principle and weak convergence problems for asymptotically nonexpansive mappings. J Korean Math Soc, 2001, 38: 1245--1260

[10] Schu J. Weak and strong convergence of fixed points of asymptotaically nonexpansive mappings. Bull Austral Math Soc, 1991, 43: 153--159

[11] Tan K K, Xu H K. Approximating fixed points of nonexpansive mappings by the Ishikawa iterative process. J Math Anal Appl, 1993, 178: 301--308

[12] 饶若峰. 渐近非扩张映像具误差的合成隐迭代序列的弱收敛和强收敛定理. 数学年刊, 2008, 29A(4): 461--470

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New Composite Implicit Iterative Scheme With Errors

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