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http://dx.doi.org/10.4134/BKMS.2010.47.6.1259

STRONG CONVERGENCE OF AN IMPLICIT ITERATIVE PROCESS FOR AN INFINITE FAMILY OF STRICT PSEUDOCONTRACTIONS  

Cho, Yeol-Je (DEPARTMENT OF MATHEMATICS EDUCATION AND RINS GYEONGSANG NATIONAL UNIVERSITY)
Kang, Shin-Min (DEPARTMENT OF MATHEMATICS AND RINS GYEONGSANG NATIONAL UNIVERSITY)
Qin, Xiaolong (DEPARTMENT OF MATHEMATICS HANGZHOU NORMAL UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.6, 2010 , pp. 1259-1268 More about this Journal
Abstract
In this paper, we consider an implicit iterative process with errors for an in nite family of strict pseudocontractions. Strong convergence theorems are established in the framework of Banach spaces. The results presented in this paper improve and extend the recent ones announced by many others.
Keywords
implicit iterative process; strict pseudocontraction; nonexpansive mapping; common fixed point; Banach space;
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1 R. Chen, Y. Song, and H. Zhou, Convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings, J. Math. Anal. Appl. 314 (2006), no. 2, 701-709.   DOI   ScienceOn
2 C. E. Chidume and N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62 (2005), no. 6, 1149-1156.   DOI   ScienceOn
3 K. Deimling, Zeros of accretive operators, Manuscripta Math. 13 (1974), 365-374.   DOI
4 F. E. Browder and W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), 197-228.   DOI
5 X. Qin, Y. J. Cho, and M. Shang, Convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings, Appl. Math. Comput. 210 (2009), no. 2, 542-550.   DOI   ScienceOn
6 H. K. Xu and R. G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001), no. 5-6, 767-773.   DOI   ScienceOn
7 L. C. Zeng and J. C. Yao, Implicit iteration scheme with perturbed mapping for common fixed points of a finite family of nonexpansive mappings, Nonlinear Anal. 64 (2006), no. 11, 2507-2515.   DOI   ScienceOn
8 H. Zhou, Convergence theorems of common fixed points for a finite family of Lipschitz pseudocontractions in Banach spaces, Nonlinear Anal. 68 (2008), no. 10, 2977-2983.   DOI   ScienceOn
9 M. O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl. 294 (2004), no. 1, 73-81.   DOI   ScienceOn
10 S. Plubtieng, K. Ungchittrakool, and R. Wangkeeree, Implicit iterations of two finite families for nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optim. 28 (2007), no. 5-6, 737-749.   DOI   ScienceOn
11 X. Qin, Y. Su, and M. Shang, On the convergence of strictly pseudo-contractive map-pings in Banach spaces, J. Prime Res. Math. 3 (2007), 154-161.
12 N. Shahzad and H. Zegeye, Strong convergence of an implicit iteration process for a finite family of generalized asymptotically quasi-nonexpansive maps, Appl. Math. Comput. 189 (2007), no. 2, 1058-1065.   DOI   ScienceOn
13 K. K. Tan and H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993), no. 2, 301-308.   DOI   ScienceOn
14 S. Thianwan and S. Suantai, Weak and strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Sci. Math. Jpn. 66 (2007), no. 1, 73-81.