CFP last date
20 May 2024
Call for Paper
June Edition
IJCA solicits high quality original research papers for the upcoming June edition of the journal. The last date of research paper submission is 20 May 2024

Submit your paper
Know more
The week's pick
Responsive image
Enhancing Privacy Preservation: Multi-Attribute Protection with P-Sensitive K-Anonymity

Twinkle Patel Kiran Amin
Random Articles
Reseach Article

Data Dependence of Noor and SP Iterative Schemes when dealing with Quasi-Contractive Operators

by Renu Chugh, Vivek Kumar
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 40 - Number 15
Year of Publication: 2012
Authors: Renu Chugh, Vivek Kumar
10.5120/5059-7384

Renu Chugh, Vivek Kumar . Data Dependence of Noor and SP Iterative Schemes when dealing with Quasi-Contractive Operators. International Journal of Computer Applications. 40, 15 ( February 2012), 41-46. DOI=10.5120/5059-7384

@article{ 10.5120/5059-7384,
author = { Renu Chugh, Vivek Kumar },
title = { Data Dependence of Noor and SP Iterative Schemes when dealing with Quasi-Contractive Operators },
journal = { International Journal of Computer Applications },
issue_date = { February 2012 },
volume = { 40 },
number = { 15 },
month = { February },
year = { 2012 },
issn = { 0975-8887 },
pages = { 41-46 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume40/number15/5059-7384/ },
doi = { 10.5120/5059-7384 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:28:11.520892+05:30
%A Renu Chugh
%A Vivek Kumar
%T Data Dependence of Noor and SP Iterative Schemes when dealing with Quasi-Contractive Operators
%J International Journal of Computer Applications
%@ 0975-8887
%V 40
%N 15
%P 41-46
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

We prove results concerning data dependence of Noor and SP iterative schemes using certain quasi-contractive operators in real Banach spaces. Our results reveal that by choosing an approximate quasi-contractive operator (for which it is possible to compute the fixed point); we can approximate the fixed point of the given operator. An example is also provided to explain the validity of our results.

References
  1. Berinde, V. : 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).
  2. Berinde, V.: Generalized Contractions and Applications , (Romanian), Editura Cub press 22, Baia Mare (1997).
  3. Chidume , C. E and Mutangadura, S. A. : An example of the Mann iteration method for Lipschitz pseudo-contractions, Proceedings of the American Mathematical Society, vol. 129, no. 8, pp. 2359-2363(2001).
  4. Chugh, Renu and Kumar, Vivek: Strong convergence of SP iterative scheme for quasi-contractive operators in Banach spaces, International Journal of Computer Applications, volume 31, No. 5, October (2011).
  5. Ciric, L.B., Lee, B. S. and Rafiq, A.: Faster Noor iterations, Indian Journal of Mathematics, T. Pati Memorial Volume , vol 52, no 3, 429- 436(2010).
  6. Imoru ,C. O. and Olatinwo, M. O. : On the stability of Picard and Mann iteration processes, Carpathian Journal of Mathematics, vol. 19, no. 2, pp. 155–160(2003).
  7. Ishikawa, S. : Fixed points by a new iteration method, Proceedings of the American Mathematical Society, vol. 44, no. 1, pp. 147–150 (1974).
  8. Mann, W. R. : Mean value methods in iteration, Proceedings of the American Mathematical Society, vol. 4, no. 3, pp. 506–510( 1953).
  9. Noor, M. A. : New approximation schemes for general variational inequalities, Journal of Mathematical Analysis and Applications, vol. 251, no. 1, pp. 217-229(2000).
  10. Osilike, M.O., Some Stability Results for Fixed Point Iteration Procedures. J.Nigerian Math.Soc. Volume 14/15(1995), 17-29.
  11. Olaleru, J.O and Akewe. H.: The equivalence of Jungck type iterations for generalized contractive-like operators in Banach space , Fasciculi Mathematici ,47-61(2011).
  12. Phuengrattana , Withunand , Suantai, Suthep : 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, 235(2011), 3006- 3014.
  13. Park, J. A.: Mann iteration process for the fixed point of strictly pseudocontractive mapping in some Banach spaces, Journal of the Korean Mathematical Society, vol. 31, no. 3, pp. 333–337(1994).
  14. Rafiq, A.: On the convergence of the three step iteration process in the class of quasi-contractive operators, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, 22, 305-309(2006).
  15. Rhoades, B.E., Fixed Point Theorems and Stability Results for Fixed Point Iteration Procedures II, Indian J. Pure Appl. Math. 24 (11) (1993), 691-703
  16. Rus, I.A. : Generalized Contractions and Applications , Cluj University Press , Cluj-Napoca(2001),3 pages.
  17. S¸oltuz, S. M.: Data dependence for Mann iteration, Octogon Math. Magazine 9 (2001), 825-828.
  18. S¸oltuz, S. M.: Data dependence for Ishikawa iteration, Lecturas Matematicas, vol. 25, no. 2, pp. 149-155, 2004.
  19. S¸oltuz , S. M.: Data dependence for Ishikawa iteration when dealing with contractive like operators., Fixed Point Theory and Applications, Volume 2008, Article Id 242916, 7 pages.
  20. Zamfirescu, T.: Fix point theorems in metric spaces, Archiv derMathematik, vol. 23, no. 1, pp. 292-298(1972).
Index Terms

Computer Science
Information Sciences

Keywords

SP iteration Noor iteration Quasi-Contractive Operators

Powered by PhDFocusTM