Common Fixed-Point Iterative Processes with Errors for Generalized Asymptotically Quasi-Nonexpansive Mappings

In this paper, we introduce a new class of iterative procedures with errors for approximating the common fixed point of two generalized asymptotically quasi-nonexpansive mappings and prove several strong convergence results for the iterative sequence with errors in Banach spaces. We not only answer the open question proposed by Zhou et al. [1], but also extend and improve some recent corresponding results in the literature.

[1]  Jen-Chih Yao,et al.  STRONG CONVERGENCE THEOREMS OF ISHIKAWA ITERATION PROCESS WITH ERRORS FOR FIXED POINTS OF LIPSCHITZ CONTINUOUS MAPPINGS IN BANACH SPACES , 2006 .

[2]  Lu-Chuan Zeng,et al.  Implicit iteration scheme with perturbed mapping for common fixed points of a finite family of nonexpansive mappings , 2006 .

[3]  Stability of iterative procedures with errors for approximating common fixed points of a couple of q-contractive-like mappings in Banach spaces , 2006 .

[4]  Lu-Chuan Zeng,et al.  STRONG CONVERGENCE THEOREMS FOR STRICTLY PSEUDOCONTRACTIVE MAPPINGS OF BROWDER-PETRYSHYN TYPE , 2006 .

[5]  Hong-Kun Xu,et al.  Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process , 1993 .

[6]  Hu Chang.  Convergence theorems of iterative sequences for asymptotically nonexpansive mapping in uniformly convex Banach space , 2002 .

[7]  Yeol Je Cho,et al.  Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings☆ , 2004 .

[8]  Yeol Je Cho,et al.  Iterative methods for nonlinear operator equations in banach spaces , 2002 .

[9]  Tomonari Suzuki.  Common fixed points of two nonexpansive mappings in Banach spaces , 2004 .

[10]  Liu Qihou.  Iterative Sequences for Asymptotically Quasi-nonexpansive Mappings , 2001 .

[11]  Muhammad Aslam Noor,et al.  Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces , 2002 .

[12]  Hong-Kun Xu,et al.  AN IMPLICIT ITERATION PROCESS FOR NONEXPANSIVE MAPPINGS , 2001 .

[13]  Liu Qihou.  Iteration Sequences for Asymptotically Quasi-nonexpansive Mapping with an Error Member of Uniform Convex Banach Space , 2002 .

[14]  William A. Kirk,et al.  A FIXED POINT THEOREM FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS , 1972 .

[15]  S. Atsushiba.  STRONG CONVERGENCE OF ITERATIVE SEQUENCES FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN BANACH SPACES , 2003 .

[16]  Lokenath Debnath,et al.  Convergence of Ishikawa Iterates of Quasi-Nonexpansive Mappings , 1997 .

[17]  Hong-Kun Xu,et al.  Fixed point iteration processes for asymptotically nonexpansive mappings , 1994 .