- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 464593, 4 pages
Faster Multistep Iterations for the Approximation of Fixed Points Applied to Zamfirescu Operators
1Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
2Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, Belgrade 11000, Serbia
3Department of Mathematics, Lahore Leads University, Lahore 54810, Pakistan
4Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 54000, Pakistan
5Department of Mathematics, Dong-A University, Pusan 614-714, Republic of Korea
Received 13 July 2013; Accepted 7 September 2013
Academic Editor: Salvador Romaguera
Copyright © 2013 Shin Min Kang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- W. R. Mann, “Mean value methods in iteration,” Proceedings of the American Mathematical Society, vol. 4, pp. 506–510, 1953.
- S. Ishikawa, “Fixed points by a new iteration method,” Proceedings of the American Mathematical Society, vol. 44, pp. 147–150, 1974.
- B. E. Rhoades and S. M. Soltuz, “The equivalence between Mann-Ishikawa iterations and multistep iteration,” Nonlinear Analysis. Theory, Methods & Applications, vol. 58, no. 1-2, pp. 219–228, 2004.
- V. Berinde, “Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators,” Fixed Point Theory and Applications, no. 2, pp. 97–105, 2004.
- T. Zamfirescu, “Fix point theorems in metric spaces,” Archiv der Mathematik, vol. 23, pp. 292–298, 1972.
- V. Berinde, “On the convergence of the Ishikawa iteration in the class of quasi contractive operators,” Acta Mathematica Universitatis Comenianae, vol. 73, no. 1, pp. 119–126, 2004.
- V. Berinde, “A convergence theorem for some mean value fixed point iteration procedures,” Demonstratio Mathematica, vol. 38, no. 1, pp. 177–184, 2005.
- G. V. R. Babu and K. N. V. V. Vara Prasad, “Mann iteration converges faster than Ishikawa iteration for the class of Zamfirescu operators,” Fixed Point Theory and Applications, vol. 2006, Article ID 49615, 6 pages, 2006.
- Y. Qing and B. E. Rhoades, “Comments on the rate of convergence between Mann and Ishikawa iterations applied to Zamfirescu operators,” Fixed Point Theory and Applications, vol. 2008, Article ID 387504, 3 pages, 2008.