CFP last date
20 December 2024
Reseach Article

Empirical Comparison of some Iteration Methods in the Class of Quasi-Contractive Operators

by Adesanmi Alao Mogbademu, Victor Odumuyiwa
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 67 - Number 15
Year of Publication: 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 },
issue_date = { April 2013 },
volume = { 67 },
number = { 15 },
month = { April },
year = { 2013 },
issn = { 0975-8887 },
pages = { 29-31 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume67/number15/11473-7082/ },
doi = { 10.5120/11473-7082 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:24:55.816017+05:30
%A Adesanmi Alao Mogbademu
%A Victor Odumuyiwa
%T Empirical Comparison of some Iteration Methods in the Class of Quasi-Contractive Operators
%J International Journal of Computer Applications
%@ 0975-8887
%V 67
%N 15
%P 29-31
%D 2013
%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
  1. N. Adaschl, B. Ernst, D. Kleim, Topological Vector Spaces, Springer- Verlag, ( 1978).
  2. 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.
  3. 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.
  4. V. Berinde, On the stability of some fixed point procedures, Bul. Stiint. Univ. Baia Mare, Ser. B, Matematica-Informatica, xviii: ( 1974), 7- 14.
  5. 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.
  6. S. Ishikawa, Fixed points by a new iteration method, Proc. Am. Math. Soc. 44 ( 1974), 147-150.
  7. W. R. Mann, Mean Value methods in iteration, Proc. Am. Math. Soc. 4 ( 1953), 506-510.
  8. J. O. Olaleru, A comparison of Picard and Mann iterations for quasi-contractive maps, Fixed point theory, Vol. 8, No. 1 ( 2007), 87-95.
  9. 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.
  10. 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 .
  11. 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 .
  12. 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.
  13. T. Zamfirescu, Fixed point theorems in metric spaces, Archiv der Mathematik. 23, (1992), 292-298.
Index Terms

Computer Science
Information Sciences

Keywords

Zamifirecu operators Quasi-contractive operators Metrizable spaces