Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: On rate of convergence of various iterative schemes | Hussain et al. Fixed Point Theory and Applications 2011 2011 45 http content 2011 1 45 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access On rate of convergence of various iterative schemes Nawab Hussain1 Arif Rafiq2 Bosko Damjanovic3 and Rade Lazovic4 Correspondence arafiq@comsats. 2Department of Mathematics COMSATS Institute of Information Technology Islamabad Pakistan Full list of author information is available at the end of the article Abstract In this note by taking an counter example we prove that the iteration process due to Agarwal et al. J. Nonlinear Convex. Anal. 8 1 61-79 2007 is faster than the Mann and Ishikawa iteration processes for Zamfirescu operators. Keywords iteration processes Zamfirescu operator 1 Introduction For a nonempty convex subset C of a normed space E and T C C a the Mann iteration process 1 is defined by the following sequence xn i X0 e Cf xn i 1 - bn Xn bnTXn n Of nf J where bn is a sequence in 0 1 . b the sequence xn defined by x0 e Cf yn 1 - b n Xn b nTXn In . Xn 1 1 - bn Xn bnTynf n Of where bn b n are sequences in 0 1 is known as the Ishikawa 2 iteration process. c the sequence xn defined by X0 e Cf yn 1 - bn Xn b nTXnf ARSnf Xn 1 1 - bn TXn bnTynf n Of where bn b n are sequences in 0 1 is known as the Agarwal et al. 3 iteration process. Definition 1. 4 Suppose that an and bn are two real convergent sequences with limits a and b respectively. Then an is said to converge faster than bn if lim n an a bn - b 0. Springer 2011 Hussain et al licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License http licenses by which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Hussain et al. Fixed Point Theory and Applications 2011 2011 45 http content 2011 1 45 Page 2 of 6 .
