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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-db0dbec2-1b7c-4193-93af-b51051da81e3

Czasopismo

Demonstratio Mathematica

Tytuł artykułu

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

Autorzy Temir, S. 
Treść / Zawartość https://www.degruyter.com/view/j/dema
Warianty tytułu
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  
Wydawca De Gruyter
Czasopismo Demonstratio Mathematica
Rocznik 2013
Tom Vol. 46, nr 4
Strony 781--793
Opis fizyczny Bibliogr. 11 poz.
Twórcy
autor Temir, S.
Bibliografia
[1] S. S. Chang, K. K. Tan, H. W. J. Lee, C. K. Chan, On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 313 (2003), 273–283.
[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.
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