Convergence of an implicit iteration process with errors for two asymptotically nonexpansive mappings

• Autorzy: Temir, S.
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to introduce an implicit iterative process with errors for approximating common fixed point of two finite families of asymptotically nonexpansive mappings in the framework of Banach space. The results presented in this paper extend and generalize the corresponding results of Qin et al. [Convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings, Appl. Math. Comp. 210 (2009), 542–550], Thakur [Weak and strong convergence of composite implicititeration process, Appl. Math. Comp. 190 (2007), 965–973] and some others.

Słowa kluczowe

PL

odwzorowania nieekspansywne asymptotyczne; punkt stały; teoria zbieżności

EN

asymptotically nonexpansive mapping; implicit iteration process; common fixed point; convergence theorem

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2013
• Tom: Vol. 46, nr 4
• Strony: 781--793
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Temir, S.

• Department of Mathematics, Art and Science Faculty, Harran University, 63200, Sanliurfa, Turkey,

Bibliografia

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• [2] C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62(6) (2005), 1149–1156.
• [3] J. Gornicki, Weak convergence theorems for asymptotically nonexpansive mappings in uniformly Banach spaces, Comment. Math. Univ. Carolin. 301 (1989), 249–252.
• [4] K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171–174.
• [5] X. Qin, Y. J. Cho, M. Shang, Convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings, Appl. Math. Comput. 210 (2009), 542–550.
• [6] J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 43 (1991), 153–159.
• [7] Z. H. Sun, Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. 286 (2003), 351–358.
• [8] K. K. Tan, H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iterative process, J. Math. Anal. Appl. 178 (1993), 301–308.
• [9] B. S. Thakur, Weak and strong convergence of composite implicit iteration process, Appl. Math. Comput. 190 (2007), 965–973.
• [10] H. K. Xu, R. G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001), 767–773.
• [11] Y. Zhou, S. S. Chang, Convergence of implicit iteration process for a finite family of asymptotically nonexpansive mappings in Banach spaces, Numerical Functional Analysis and Optimization 23 (2002), 911–921.