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Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero


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CiteScore 2017: 0.28
SCImago Journal Rank (SJR) 2017: 0.231
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Mathematical Citation Quotient (MCQ) 2017: 0.12
ICV 2017: 121.78



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2391-4661
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Volume 46, Issue 4

Issues

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

Seyit Temir
Published Online: 2017-05-10 | DOI: https://doi.org/10.1515/dema-2013-0480

Abstract

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 implicit iteration process, Appl. Math. Comp. 190 (2007), 965–973] and some others.

Keywords: asymptotically nonexpansive mapping; implicit iteration process; common fixed point; convergence theorems

MSC 2010: 47H09; 47H10

References

  • [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.Google Scholar

  • [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.Google Scholar

  • [3] J. Gornicki, Weak convergence theorems for asymptotically nonexpansive mappings in uniformly Banach spaces, Comment. Math. Univ. Carolin. 301 (1989), 249–252.Google Scholar

  • [4] K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171–174.Google Scholar

  • [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.Web of ScienceGoogle Scholar

  • [6] J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 43 (1991), 153–159.Google Scholar

  • [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.Google Scholar

  • [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.Google Scholar

  • [9] B. S. Thakur, Weak and strong convergence of composite implicit iteration process, Appl. Math. Comput. 190 (2007), 965–973.Web of ScienceGoogle Scholar

  • [10] H. K. Xu, R. G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001), 767–773.Web of ScienceGoogle Scholar

  • [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.Google Scholar

About the article

Received: 2011-06-12

Published Online: 2017-05-10

Published in Print: 2013-12-01


Citation Information: Demonstratio Mathematica, Volume 46, Issue 4, Pages 781–793, ISSN (Online) 2391-4661, DOI: https://doi.org/10.1515/dema-2013-0480.

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© 2013 Seyit Temir, published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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