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Strong Convergence and Stability results for Jungck-SP iterative scheme

by Renu Chugh, Vivek Kumar
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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

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