We apologize for a recent technical issue with our email system, which temporarily affected account activations. Accounts have now been activated. Authors may proceed with paper submissions. PhDFocusTM
CFP last date
20 December 2024
Reseach Article

Strong Convergence and Stability results for Jungck-SP iterative scheme

by Renu Chugh, Vivek Kumar
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 36 - Number 12
Year of Publication: 2011
Authors: Renu Chugh, Vivek Kumar
10.5120/4555-6460

Renu Chugh, Vivek Kumar . Strong Convergence and Stability results for Jungck-SP iterative scheme. International Journal of Computer Applications. 36, 12 ( December 2011), 40-46. DOI=10.5120/4555-6460

@article{ 10.5120/4555-6460,
author = { Renu Chugh, Vivek Kumar },
title = { Strong Convergence and Stability results for Jungck-SP iterative scheme },
journal = { International Journal of Computer Applications },
issue_date = { December 2011 },
volume = { 36 },
number = { 12 },
month = { December },
year = { 2011 },
issn = { 0975-8887 },
pages = { 40-46 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume36/number12/4555-6460/ },
doi = { 10.5120/4555-6460 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:23:05.416556+05:30
%A Renu Chugh
%A Vivek Kumar
%T Strong Convergence and Stability results for Jungck-SP iterative scheme
%J International Journal of Computer Applications
%@ 0975-8887
%V 36
%N 12
%P 40-46
%D 2011
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, we study strong convergence as well as stability results for a pair of nonself mappings using Jungck-SP iterative scheme and a certain contractive condition. Moreover, with the help of computer programs in C++, we show that Jungck-SP iterative scheme converges faster than Jungck-Noor, Jungck-Ishikawa and Jungck-Mann iterative schemes through example.

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.: Iterative Approximation of Fixed Points, Editura Efemeride (2002).
  3. Bosede, A. O.: Strong convergence results for the Jungck-Ishikawa and Jungck-Mann iteration processes, Bulletin of Mathematical Analysis and Applications 2, 3 (2010), 65–73.
  4. Bosede, A. O., Rhoades, B. E.: Stability of Picard and Mann iterations for a general class of functions. Journal of Advanced Mathematical Studies 3, 2 (2010), 1–3.
  5. Chugh, Renu and Kumar, Vivek: Strong convergence of SP iterative scheme for quasi-contractive operators in Banach spaces, International Journal of Computer Aplications, volume 31, No. 5 , Octomber (2011).
  6. Harder ,A. M. and Hicks, T. L.: Stability Results for Fixed Point Iteration Procedures, Math. Japonica 33 (5) (1988), 693-706.
  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. Jungck, G. : Commuting mappings and fixed points, The American Mathematical Monthly, vol. 83, no.4, pp. 261–263(1976).
  9. Mann, W. R.: Mean value methods in iteration, Proceedings of the American Mathematical Society, vol.4, pp. 506–510( 1953).
  10. Noor, M. A. : New approximation schemes for general variational inequalities, Journal of Mathematical Analysis and Applications, vol. 251, no. 1, pp. 217–229(2000).
  11. Olatinwo , M. O. and Imoru, C. O.: Some convergence results for the Jungck-Mann and the Jungck-Ishikawa iteration processes in the class of generalized Zamfirescu operators, Acta Mathematica Universitatis Comenianae, vol. 77, no. 2, pp. 299–304( 2008).
  12. Olatinwo, M. O.: Some stability and strong convergence results for the Jungck-Ishikawa iteration process, Creative Mathematics and Informatics, vol. 17, pp. 33–42(2008).
  13. Olatinwo, M. O.: A generalization of some convergence results using the Jungck-Noor three-step iteration process in an arbitrary Banach space, Fasciculi Mathematici, no. 40, pp. 37–43( 2008).
  14. Osilike, M. O. : Stability results for the Ishikawa fixed point iteration procedure, Indian Journal of Pure and Applied Mathematics, vol. 26, no. 10, pp. 937–945 (1995).
  15. Osilike , M.O. and Udomene, A. : Short Proofs of Stability Results for Fixed Point Iteration Procedures for a Class of Contractive-type Mappings, Indian J. Pure Appl. Math. 30 (12) (1999), 1229-1234
  16. Ostrowski, A. M.: The Round-off Stability of Iterations, Z. Angew. Math. Mech. 47 (1967), 77-81.
  17. 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.
  18. P., Bhagwati and S., Ritu: Weak stability results for Jungck-Ishikawa iteration, International Journal of Computer Applications, Volume16, No. 4, February (2011).
  19. Rhoades, B. E.: Comments on two fixed point iteration methods,” Journal of Mathematical Analysis and Applications, vol. 56, no. 3, pp. 741–750(1976).
  20. Singh, S. L. , Bhatnagar, Charu and Mishra, S. N.: Stability of Jungck-type iterative procedures, International Journal of Mathematics and Mathematical Sciences, no. 19, pp. 3035–3043 (2005).
  21. Zamfirescu, T.: Fixed point theorems in metric spaces, Arch. Math., 23(1972), 292-298.
Index Terms

Computer Science
Information Sciences

Keywords

Jungck-SP iteration Jungck-Ishikawa iteration Jungck-Noor iteration Stability