Most Read Research Articles


Warning: Creating default object from empty value in /var/www/html/sandbox.ijcaonline.org/public_html/modules/mod_mostread/helper.php on line 79

Warning: Creating default object from empty value in /var/www/html/sandbox.ijcaonline.org/public_html/modules/mod_mostread/helper.php on line 79

Warning: Creating default object from empty value in /var/www/html/sandbox.ijcaonline.org/public_html/modules/mod_mostread/helper.php on line 79

Warning: Creating default object from empty value in /var/www/html/sandbox.ijcaonline.org/public_html/modules/mod_mostread/helper.php on line 79

Warning: Creating default object from empty value in /var/www/html/sandbox.ijcaonline.org/public_html/modules/mod_mostread/helper.php on line 79
Call for Paper - May 2015 Edition
IJCA solicits original research papers for the May 2015 Edition. Last date of manuscript submission is April 20, 2015. Read More

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

Print
PDF
International Journal of Computer Applications
© 2012 by IJCA Journal
Volume 40 - Number 15
Year of Publication: 2012
Authors:
Renu Chugh
Vivek Kumar
10.5120/5059-7384

Renu Chugh and Vivek Kumar. Article: Data Dependence of Noor and SP Iterative Schemes when dealing with Quasi-Contractive Operators. International Journal of Computer Applications 40(15):41-46, February 2012. Full text available. BibTeX

@article{key:article,
	author = {Renu Chugh and Vivek Kumar},
	title = {Article: Data Dependence of Noor and SP Iterative Schemes when dealing with Quasi-Contractive Operators},
	journal = {International Journal of Computer Applications},
	year = {2012},
	volume = {40},
	number = {15},
	pages = {41-46},
	month = {February},
	note = {Full text available}
}

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

  • 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).
  • Berinde, V.: Generalized Contractions and Applications , (Romanian), Editura Cub press 22, Baia Mare (1997).
  • 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).
  • 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).
  • 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).
  • 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).
  • Ishikawa, S. : Fixed points by a new iteration method, Proceedings of the American Mathematical Society, vol. 44, no. 1, pp. 147–150 (1974).
  • Mann, W. R. : Mean value methods in iteration, Proceedings of the American Mathematical Society, vol. 4, no. 3, pp. 506–510( 1953).
  • Noor, M. A. : New approximation schemes for general variational inequalities, Journal of Mathematical Analysis and Applications, vol. 251, no. 1, pp. 217-229(2000).
  • Osilike, M.O., Some Stability Results for Fixed Point Iteration Procedures. J.Nigerian Math.Soc. Volume 14/15(1995), 17-29.
  • 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).
  • 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.
  • 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).
  • 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).
  • 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
  • Rus, I.A. : Generalized Contractions and Applications , Cluj University Press , Cluj-Napoca(2001),3 pages.
  • S¸oltuz, S. M.: Data dependence for Mann iteration, Octogon Math. Magazine 9 (2001), 825-828.
  • S¸oltuz, S. M.: Data dependence for Ishikawa iteration, Lecturas Matematicas, vol. 25, no. 2, pp. 149-155, 2004.
  • 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.
  • Zamfirescu, T.: Fix point theorems in metric spaces, Archiv derMathematik, vol. 23, no. 1, pp. 292-298(1972).