Browse > Article
http://dx.doi.org/10.4134/CKMS.2009.24.4.539

STRONG CONVERGENCE OF MODIFIED HYBRID ALGORITHM FOR QUASI-φ-ASYMPTOTICALLY NONEXPANSIVE MAPPINGS  

Zhang, Huancheng (DEPARTMENT OF MATHEMATICS TIANJIN POLYTECHNIC UNIVERSITY)
Su, Yongfu (DEPARTMENT OF MATHEMATICS TIANJIN POLYTECHNIC UNIVERSITY)
Publication Information
Communications of the Korean Mathematical Society / v.24, no.4, 2009 , pp. 539-551 More about this Journal
Abstract
In this paper, we propose a modified hybrid algorithm and prove strong convergence theorems for a family of quasi-$\phi$-asymptotically nonexpansive mappings. Our results extend and improve the results by Nakajo, Takahashi, Kim, Xu, Su and some others.
Keywords
hybrid algorithm; quasi-$\phi$-asymptotically nonexpansive; strong convergence; generalized projection;
Citations & Related Records

Times Cited By SCOPUS : 2
연도 인용수 순위
1 Ya. I. Alber, Metric and generalized projection operators in Banach spaces: properties and applications, in: A. G. Kartsatos (Ed.), Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, Marcel Dekker, New York, 1996, 15-50
2 Ya. I. Alber and S. Reich, An iterative method for solving a class of nonlinear operator equations in Banach spaces, Panamer. Math. J. 4 (1994), 39-54
3 I. Cioranescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, Kluwer, Dordrecht, 1990
4 M. Y. Carlos and H. K. Xu, Strong convergence of the CQ method for fixed point iteration process, Nonlinear Anal. 64 (2006), 2240–2411   DOI   ScienceOn
5 Y. Haugazeau, Sur les inequations variationnelles et la minimisation de fonctionnelles convexes, These, Universite de Paris, Paris, France.
6 K. Nakajo and W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semi-groups, J. Math. Anal. Appl. 279 (2003), 372–379   DOI   ScienceOn
7 T. H. Kim and H. K. Xu, Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Analysis 64 (2006), 1140–1152   DOI   ScienceOn
8 H. Y. Zhou, Y. J. Cho, and S. M. Kang, A new iterative algorithm for approximating common fixed points for asymptotically nonexpansive mappings, Fixed Point Theory and Applications 2007 (2007), doi:10.1155/2007/64874.   DOI
9 K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171–174   DOI
10 S. Kamimura and W. Takahashi, Strong convergence of a proximal-type algorithm in a Banach space, SIAM J. Optim. 13 (2002), 938–945   DOI   ScienceOn
11 J. Schu, Iteration construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 158 (1991), 407–413   DOI
12 Y. F. Su and X. L. Qin, Strong convergence of modified Ishikawa iterations for nonlinear mappings, Proc. Indian Acad. Sci.(Math.Sci.) 117 (2007), 97–107   DOI   ScienceOn
13 W. Takahashi, Nonlinear Functional Analysis, Yokohama-Publishers, 2000.