Research Article
Empirical Comparison of some Iteration Methods in the Class of Quasi-Contractive Operators
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 67 - Issue 15 |
| Published: April 2013 |
| Authors: Adesanmi Alao Mogbademu, Victor Odumuyiwa |
10.5120/11473-7082
|
Adesanmi Alao Mogbademu, Victor Odumuyiwa . Empirical Comparison of some Iteration Methods in the Class of Quasi-Contractive Operators. International Journal of Computer Applications. 67, 15 (April 2013), 29-31. DOI=10.5120/11473-7082
@article{ 10.5120/11473-7082,
author = { Adesanmi Alao Mogbademu,Victor Odumuyiwa },
title = { Empirical Comparison of some Iteration Methods in the Class of Quasi-Contractive Operators },
journal = { International Journal of Computer Applications },
year = { 2013 },
volume = { 67 },
number = { 15 },
pages = { 29-31 },
doi = { 10.5120/11473-7082 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2013
%A Adesanmi Alao Mogbademu
%A Victor Odumuyiwa
%T Empirical Comparison of some Iteration Methods in the Class of Quasi-Contractive Operators%T
%J International Journal of Computer Applications
%V 67
%N 15
%P 29-31
%R 10.5120/11473-7082
%I Foundation of Computer Science (FCS), NY, USA
Abstract
In this paper, a new modified two-step iterative method for approximating fixed points of quasi-contractive operators is presented. It is demonstrated with some examples using an empirical approach that this iteration method performs better than some well known iterations for quasi-contractive operators satisfying Zamfirescus conditions.
References
- N. Adaschl, B. Ernst, D. Kleim, Topological Vector Spaces, Springer- Verlag, ( 1978).
- R. P. Agarwal, D. O'Regan, D. R. Sahu , Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J Nonlinear Convex Anal. 8 ( 2007)(1), 61-79.
- GVR. Babu, KNVVV. Prasad, Mann iteration converges faster than Ishikawa iteration for the class of Zamfirescu operators, Fixed Point Theory Appl, ( 2006), 1-6 . Article ID 49615.
- V. Berinde, On the stability of some fixed point procedures, Bul. Stiint. Univ. Baia Mare, Ser. B, Matematica-Informatica, xviii: ( 1974), 7- 14.
- N. Hussain, A. Rafiq, B. Damjanovi and R. Lazovi, On rate of convergence of various iterative schemes, Fixed Point Theory and Applications , 45( 2011), 1-6.
- S. Ishikawa, Fixed points by a new iteration method, Proc. Am. Math. Soc. 44 ( 1974), 147-150.
- W. R. Mann, Mean Value methods in iteration, Proc. Am. Math. Soc. 4 ( 1953), 506-510.
- J. O. Olaleru, A comparison of Picard and Mann iterations for quasi-contractive maps, Fixed point theory, Vol. 8, No. 1 ( 2007), 87-95.
- J. O. Olaleru and A. A. Mogbademu, On the stability of some fixed point iteration procedures with errors , Boletino de la Asociacion Matematica Venezolana, Vol. XVI, No. 1 ( 2009), 31-37.
- M. O. Olatinwo and C. O. Imoru, On some stability results for fixed point iteration procedure, Journal of Math. and Stat. 2(1), ( 2006), 339-342 .
- B. E. Rhoades, Fixed point theorems and stability results for fixed point iteration procedures I, Indian J. Pure and Applied Math. , 21, ( 1990), 1-9 .
- I. Yildirim, M. Ozdemir and H. Kiziltun¸ On the Convergence of a New Two-Step Iteration in the Class of Quasi-Contractive Operators, Int. Journal of Math. Analysis, Vol. 3, ( 2009), no. 38, 1881 - 1892.
- T. Zamfirescu, Fixed point theorems in metric spaces, Archiv der Mathematik. 23, (1992), 292-298.
Index Terms
Keywords