About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 132626, 15 pages
http://dx.doi.org/10.1155/2013/132626
Research Article

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.

Linked References

  1. G. Jungck, “Commuting mappings and fixed points,” The American Mathematical Monthly, vol. 83, no. 4, pp. 261–263, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. 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. View at Zentralblatt MATH · View at MathSciNet
  4. 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. View at MathSciNet
  5. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  6. 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. View at Zentralblatt MATH · View at MathSciNet
  7. 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.
  8. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. A. Noor, “New approximation schemes for general variational inequalities,” Journal of Mathematical Analysis and Applications, vol. 251, no. 1, pp. 217–229, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. Ishikawa, “Fixed points by a new iteration method,” Proceedings of the American Mathematical Society, vol. 44, no. 1, pp. 147–150, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. W. R. Mann, “Mean value methods in iteration,” Proceedings of the American Mathematical Society, vol. 4, pp. 506–510, 1953. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. 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. View at Zentralblatt MATH · View at MathSciNet
  13. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  14. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  16. 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.
  17. G. Jungck and N. Hussain, “Compatible maps and invariant approximations,” Journal of Mathematical Analysis and Applications, vol. 325, no. 2, pp. 1003–1012, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. 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. View at Zentralblatt MATH · View at MathSciNet
  19. 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.
  20. 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. View at MathSciNet
  21. B. E. Rhoades, “Comments on two fixed point iteration methods,” Journal of Mathematical Analysis and Applications, vol. 56, no. 3, pp. 741–750, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. S. L. Singh, “A new approach in numerical praxis,” Progress of Mathematics, vol. 32, no. 2, pp. 75–89, 1998. View at Zentralblatt MATH · View at MathSciNet
  23. 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. View at MathSciNet
  24. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  25. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  26. S. H. Khan, A. Rafiq, and N. Hussain, “A three-step iterative scheme for solving nonlinear ϕ-strongly accretive operator equations in Banach spaces,” Fixed Point Theory and Applications, vol. 2012, article 149, 2012.
  27. 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. View at Zentralblatt MATH · View at MathSciNet
  28. M. F. Barnsley, Fractals Everywhere, Academic Press Professional, Boston, Mass, USA, 2nd edition, 1993. View at MathSciNet