Research Article
Remarks on Convergence among Picard, Mann and Ishikawa Iteration for Complex Space
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 21 - Issue 9 |
| Published: May 2011 |
| Authors: Rajeshri Rana, R.C.Dimri, Anita Tomar |
10.5120/2540-3475
|
Rajeshri Rana, R.C.Dimri, Anita Tomar . Remarks on Convergence among Picard, Mann and Ishikawa Iteration for Complex Space. International Journal of Computer Applications. 21, 9 (May 2011), 20-29. DOI=10.5120/2540-3475
@article{ 10.5120/2540-3475,
author = { Rajeshri Rana,R.C.Dimri,Anita Tomar },
title = { Remarks on Convergence among Picard, Mann and Ishikawa Iteration for Complex Space },
journal = { International Journal of Computer Applications },
year = { 2011 },
volume = { 21 },
number = { 9 },
pages = { 20-29 },
doi = { 10.5120/2540-3475 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2011
%A Rajeshri Rana
%A R.C.Dimri
%A Anita Tomar
%T Remarks on Convergence among Picard, Mann and Ishikawa Iteration for Complex Space%T
%J International Journal of Computer Applications
%V 21
%N 9
%P 20-29
%R 10.5120/2540-3475
%I Foundation of Computer Science (FCS), NY, USA
Abstract
In this paper we have drawn a comparative analysis among convergence of Picard, Mann and Ishikawa iteration for the complex space.
References
- G.V.R Babu and K.N.V.V. Vara Prashad, “Mann iteration converges faster than Ishikawa iteration for the class of Zamfirescu Operators”, Fixed Point Theory and Applications, Vol. 2006, Art. ID 49615, 6 pages.
- V. Berinde, “Picard’s iteration converges faster than Mann iteration for a class of Quasi-Contractive Operators”, Fixed Point Theory and Application, Vol. 2004, No. 2. 97-105.
- Y. S. Chauhan, R. Rana and A. Negi, “New Julia Sets of Ishikawa Iterates”, International Journal of Computer Applications 7(13):34–42, October 2010.
- K. Deimling, “Nonlinear Functional Analysis”, Springer Verlag, Berlin, 1985.
- S. Ishikawa, “Fixed points by a new iteration method”, Proc. Amer. Math. Soc.44 (1974), 147-150.
- W. R. Mann, “Mean value methods in iteration”, Proc. Amer. Math. Soc. 4(1953), 506-510.
- R. Rana, Y. S. Chauhan and A. Negi, Non Linear dynamics of Ishikawa Iteration, International Journal of Computer Applications 7(13):43–49, October 2010.
- B. E. Rhoades and S. M. Soltuz, “The convergence of mean value iteration for a family of maps”, I. J. M. M. S., (2005), 3479-3485.
- Xue Zhiqun, “ Remarks of equivalence among Picard, Mann and Ishikawa iterations in Normed Spaces”, Fixed Point Theory and Applications, Vol. 2007, ArticleId 61434, 5 pages.
- Xue Zhiqun, “On the convergence between Mann iteration and Ishikawa iteration for the Generalized Lipschitizan and -strongly pseudocontractive mappings”, Bull. Korean Math. Soc. 45 (2008), No. 4, pp- 635-644.
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