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Remarks on Convergence among Picard, Mann and Ishikawa Iteration for Complex Space
by
Rajeshri Rana,
R.C.Dimri,
Anita Tomar
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 21 - Number 9 |
| Year of Publication: 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
},
issue_date = { May 2011 },
volume = { 21 },
number = { 9 },
month = { May },
year = { 2011 },
issn = { 0975-8887 },
pages = {
20-29
},
numpages = {9},
url = {
https://ijcaonline.org/archives/volume21/number9/2540-3475/
},
doi = { 10.5120/2540-3475 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:08:02.619537+05:30
%A Rajeshri Rana
%A R.C.Dimri
%A Anita Tomar
%T Remarks on Convergence among Picard, Mann and Ishikawa Iteration for Complex Space
%J International Journal of Computer Applications
%@ 0975-8887
%V 21
%N 9
%P 20-29
%D 2011
%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.
Index Terms
Computer Science
Information Sciences
Keywords