Journal of Applied Mathematics
Volume 2012 (2012), Article ID 526503, 22 pages
http://dx.doi.org/10.1155/2012/526503
Research Article

On the Rate of Convergence of Kirk-Type Iterative Schemes

Nawab Hussain,1 Renu Chugh,2 Vivek Kumar,2 and Arif Rafiq3

1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, M. D. University, Rohtak 124001, India
3Hajvery University, 43-52 Industrial Area, Gulberg-III, Lahore, Pakistan

Received 29 January 2012; Revised 21 April 2012; Accepted 14 May 2012

Academic Editor: B. V. Rathish Kumar

Copyright © 2012 Nawab Hussain et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The purpose of this paper is to introduce Kirk-type new iterative schemes called Kirk-SP and Kirk-CR schemes and to study the convergence of these iterative schemes by employing certain quasi-contractive operators. By taking an example, we will compare Kirk-SP, Kirk-CR, Kirk-Mann, Kirk-Ishikawa, and Kirk-Noor iterative schemes for aforementioned class of operators. Also, using computer programs in C++, we compare the above-mentioned iterative schemes through examples of increasing, decreasing, sublinear, superlinear, and oscillatory functions.