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Abstrakty
The purpose of this paper is to study the weak and strong convergence of an new implicit iteration process to a common fixed point for a finite family of asymptotically nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve important known results in [1], [2], [4]-[9], [11]-[15] and others.
Wydawca
Czasopismo
Rocznik
Tom
Strony
267--282
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- Institute of Applied Mathematics Hangzhou Teacher's College Hangzhou, Zhejiang 310036 P. R. China, gufeng99@sohu.com
Bibliografia
- [1] Bauschke, H. H., The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 202 (1996), 150-159.
- [2] Chang, S. S., Cho, Y. J., The implicit iterative processes for asymptotically nonexpansive mappings, Nonlinear Anal. Appl. 1 (2003), 369-382.
- [3] Chang, S. S., Cho, Y. J., Zhou, H. Y., Demi-closed principle and weak convergence problems for asymptotically nonexpansive mappings, J. Korean Math. Soc. 38 (2001), 1245-1260.
- [4] Goebel, K., Kirk, W. A., A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171-174.
- [5] Górnicki, J., Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces, Comment. Math. Univ. Carolin. 301 (1989), 249-252.
- [6] Halpern, B., Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 13 (1967), 957-961.
- [7] Lions, P. L., Approximation de points fixes de contractions, C. R. Acad. Sci. Paris Ser. I Math. 284 (1977), 1357-1359.
- [8] Osilike, M. O., Implicit iteration process for common fixed point of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl. 294 (2004), 73-81.
- [9] Reich, S., Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 15 (1980), 287-292.
- [10] Schu, J., Weak and strong convergence of fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 43 (1991), 153-159.
- [11] Sun, Z. H., Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. 286 (2003), 351-358.
- [12] Tan, K. K., Xu, H. K., The nonlinear ergodic theorem for asymptotically nonexpansive mappings in Banach spaces, Proc. Amer. Math. Soc. 114 (1992), 399-404.
- [13] Wittmann, R., Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992), 486-491.
- [14] Xu, H. K., Ori, M. G., An implicit iterative process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001), 767-773.
- [15] 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. 23 (2002), 911-921.
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Bibliografia
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bwmeta1.element.baztech-article-LOD4-0002-0029