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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 132626, 15 pages
On Rate of Convergence of Jungck-Type Iterative Schemes
1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, M.D. University, Rohtak 124001, India
Received 27 February 2013; Accepted 3 April 2013
Academic Editor: Yisheng Song
Copyright © 2013 Nawab Hussain 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.
- G. Jungck, “Commuting mappings and fixed points,” The American Mathematical Monthly, vol. 83, no. 4, pp. 261–263, 1976.
- S. L. Singh, C. Bhatnagar, and S. N. Mishra, “Stability of Jungck-type iterative procedures,” International Journal of Mathematics and Mathematical Sciences, no. 19, pp. 3035–3043, 2005.
- M. O. Olatinwo, “Some stability and strong convergence results for the Jungck-Ishikawa iteration process,” Creative Mathematics and Informatics, vol. 17, pp. 33–42, 2008.
- A. O. Bosede, “Strong convergence results for the Jungck-Ishikawa and Jungck-Mann iteration processes,” Bulletin of Mathematical Analysis and Applications, vol. 2, no. 3, pp. 65–73, 2010.
- J. O. Olaleru and H. Akewe, “On multistep iterative scheme for approximating the common fixed points of contractive-like operators,” International Journal of Mathematics and Mathematical Sciences, vol. 2010, Article ID 530964, 11 pages, 2010.
- M. O. Olatinwo, “A generalization of some convergence results using a Jungck-Noor three-step iteration process in arbitrary Banach space,” Polytechnica Posnaniensis, no. 40, pp. 37–43, 2008.
- R. Chugh and V. Kumar, “Strong Convergence and Stability results for Jungck-SP iterative scheme,” International Journal of Computer Applications, vol. 36, no. 12, 2011.
- W. Phuengrattana and S. Suantai, “On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval,” Journal of Computational and Applied Mathematics, vol. 235, no. 9, pp. 3006–3014, 2011.
- M. A. Noor, “New approximation schemes for general variational inequalities,” Journal of Mathematical Analysis and Applications, vol. 251, no. 1, pp. 217–229, 2000.
- S. Ishikawa, “Fixed points by a new iteration method,” Proceedings of the American Mathematical Society, vol. 44, no. 1, pp. 147–150, 1974.
- W. R. Mann, “Mean value methods in iteration,” Proceedings of the American Mathematical Society, vol. 4, pp. 506–510, 1953.
- R. P. Agarwal, D. O'Regan, and D. R. Sahu, “Iterative construction of fixed points of nearly asymptotically nonexpansive mappings,” Journal of Nonlinear and Convex Analysis, vol. 8, no. 1, pp. 61–79, 2007.
- D. R. Sahu and A. Petruşel, “Strong convergence of iterative methods by strictly pseudocontractive mappings in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 17, pp. 6012–6023, 2011.
- 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.
- 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.
- N. Hussain, G. Jungck, and M. A. Khamsi, “Nonexpansive retracts and weak compatible pairs in metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 100, 2012.
- G. Jungck and N. Hussain, “Compatible maps and invariant approximations,” Journal of Mathematical Analysis and Applications, vol. 325, no. 2, pp. 1003–1012, 2007.
- 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.
- R. Chugh and V. Kumar, “Convergence of SP iterative scheme with mixed errors for accretive Lipschitzian and strongly accretive Lipschitzian operators in Banach space,” International Journal of Computer Mathematics, vol. 2013, 17 pages, 2013.
- N. Hussain, A. Rafiq, B. Damjanović, and R. Lazović, “On rate of convergence of various iterative schemes,” Fixed Point Theory and Applications, vol. 45, 6 pages, 2011.
- B. E. Rhoades, “Comments on two fixed point iteration methods,” Journal of Mathematical Analysis and Applications, vol. 56, no. 3, pp. 741–750, 1976.
- S. L. Singh, “A new approach in numerical praxis,” Progress of Mathematics, vol. 32, no. 2, pp. 75–89, 1998.
- N. Hussain, R. Chugh, V. Kumar, and A. Rafiq, “On the rate of convergence of Kirk-type iterative schemes,” Journal of Applied Mathematics, Article ID 526503, 22 pages, 2012.
- N. Hussain, A. Rafiq, L. B. Ciric, and S. Al-Mezel, “Almost stability of the Mann type iteration method with error term involving strictly hemicontractive mappings in smooth Banach spaces,” Journal of Inequalities and Applications, vol. 2012, article 207, 2012.
- N. Hussain, A. Rafiq, and L. B. Ciric, “Stability of the Ishikawa iteration scheme with errors for two strictly hemicontractive operators in Banach spaces,” Fixed Point Theory and Applications, vol. 2012, article 160, 2012.
- S. H. Khan, A. Rafiq, and N. Hussain, “A three-step iterative scheme for solving nonlinear -strongly accretive operator equations in Banach spaces,” Fixed Point Theory and Applications, vol. 2012, article 149, 2012.
- Y. Song and X. Liu, “Convergence comparison of several iteration algorithms for the common fixed point problems,” Fixed Point Theory and Applications, vol. 2009, Article ID 824374, 13 pages, 2009.
- M. F. Barnsley, Fractals Everywhere, Academic Press Professional, Boston, Mass, USA, 2nd edition, 1993.