On the Rate of Convergence of Some New Modified Iterative Schemes

Renu Chugh, Sanjay Kumar

Department of Mathematics, M.D.U, Rohtak, India.

DOI: 10.4236/ajcm.2013.34037                

Abstract

In this article, following Bizare and Amriteimoori [1] and B. Parsad and R. Sahni [2], we modify Ishikawa, Agarwal et al., Noor, SP iterative schemes and compare the rate of convergence of Ishikawa, Agarwal et al., Noor, SP and new modified Ishikawa, Agarwal et al., Noor, SP iterative schemes not only for particular fixed value of a_n,b_n,r_{n but also for varying the value of an,bn,rn. With the help of two numerical examples, we compare the converging step.}

Keywords

Metric Space; New Modified Ishikawa; New Modified Agarwal et al.; New Modified SP; New Modified Noor

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. Biazar and A. Amirteimoori, “An Improvement to the Fixed Point Iterative Method,” Applied Mathematics and Computation, Vol. 182, No. 1, 2006, pp. 567-571. http://dx.doi.org/10.1016/j.amc.2006.04.019
[2]	B. Prasad and R. Sahni, “Convergence of Some General Iterative Schemes,” International Journal of Mathematical Analysis, Vol. 5, No. 25, 2011, pp. 1237-1242.
[3]	S. Ishikawa, “Fixed Points by a New Iteration Method,” Proceedings of the American Mathematical Society, Vol. 44, No. 1, 1974, pp. 147-150. http://dx.doi.org/10.1090/S0002-9939-1974-0336469-5
[4]	R. P. Agarwal, D. O’Regan and D. R. Sahu, “Iterative Construction of Fixed Points of Nearly Asymptotically Non-Expansive Mappings,” Journal of Nonlinear and Convex Analysis, Vol. 8, No. 1, 2007, pp. 61-79.
[5]	M. A. Noor, “New Approximation Schemes for General Variational Inequalities,” Journal of Mathematical Analysis and Applications, Vol. 251, No. 1, 2000, pp. 217-229. http://dx.doi.org/10.1006/jmaa.2000.7042
[6]	W. Phuengrattana and S. Suantai, “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, Vol. 235, No. 9, 2011, pp. 3006-3014. http://dx.doi.org/10.1016/j.cam.2010.12.022
[7]	E. Babolian and J. Biazar, “On the Order of Convergence of Adomian Method,” Applied Mathematics and Computation, Vol. 130, No. 2-3, 2002, pp. 383-387. http://dx.doi.org/10.1016/S0096-3003(01)00103-5