Generalized three-step iteration schemes and common fixed points of three asymptotically quasi-nonexpansive mappings

• Autorzy: Rashwan R. , Hakim A.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we study strong convergence theorems for a generalized three-step iterative scheme with errors to approximate common fixed points of three asymptotically quasi-nonexpansive mappings in real Banach spaces. Our results generalize and improve upon the corresponding results in [1], [2], [3], [4], [5], [6], [7], [9], [13] and [16]. As an application of our results, we give and prove strong convergence theorems in uniformly convex Banach spaces.

Słowa kluczowe

EN

Banach space; asymtotically quasinonexpansive mapping; strong convergence

PL

przestrzeń Banacha; punkt stały; odwzorowania

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 4
• Strony: 895--908
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Rashwan R.

autor

Hakim A.

• Assiut University Faculty of Science Mathematics Department Assiut, Egypt,

Bibliografia

• [1] Y. J. Cho, H. Zhou, G. Guo, Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl. 47 (2004), 707-717.
• [2] H. Fukhar-ud-din, S. H. Khan, Convergence of two-step iterative scheme with errors for two asymptotically nonexpansive mappings, Int, J. Math. Sci. 37 (2004), 1956-1971.
• [3] H. Fukhar-ud-din, S. H. Khan, Convergence of iterates with errors for asymptotically quasi-nonexpansive mappings and applications, J. Math. Anal. Appl. 328 (2007), 821-829.
• [4] Z. Huang, Mann and Ishikawa iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl. 37 (1999), 1-7.
• [5] J. U. Jeong and S. H. Kim, Weak and strong convergence of the Ishikawa iteration process with errors for two asymptotically nonexpansive mappings, Appl. Math. Comp. 181(2006), 1394-1401.
• [6] S. H. Khan and W. Takahashi, Approximating common fixed points of two asymptotically nonexpansive mappings, Sci. Math. Jpn. 53 (2001), 143-148.
• [7] S. H. Khan, H. Fukhar-ud-din,Weak and strong convergence of a scheme with errors for two nonexpansive mappings, Nonlinear Anal. 61 (2005), 1295-1301.
• [8] L. S. Liu, Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194(1) (1995), 114-125.
• [9] L. Qihou, Iterative sequences for asymptotically quasi-nonexpansive mappings with errors member, J. Math. Anal. Appl. 259 (2001), 18-24.
• [10] R. A. Rashwan, A. A. Abdel Hakim, Weak and Strong Convergence Theorems for Three-Step Iterations with Errors for Three Asymptotically Nonexpansive Mappings, (submitted).
• [11] J. Schu, Weak and strong convergence of fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 43(1991), 153-159.
• [12] H. F. Senter and W. G. Dotson, Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 44 (1974), 375-379.
• [13] W. Takahashi and T. Tamura, Convergence theorems for a pair of nonexpansive mappings, J. Convex Analysis 5(1) (1998), 45-48.
• [14] K. K. Tan, H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993), 301-308.
• [15] Y. G. Xu, Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224(1998), 1-101.
• [16] B. L. Xu, M. A. Noor, Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002), 444-453.