S-iteration process for quasi-contractive mappings

Author:

Kumar Vivek,Latif Abdul,Rafiq Arif,Hussain Nawab

Abstract

Abstract In this note, we show that the S-iteration process due to Sahu and Petrusel (Nonlinear Anal. TMA 74(17):6012-6023, 2011) is faster than the Picard, Mann, Ishikawa and Noor iteration processes for Zamfirescu operators. Also, using computer programs in C + + , we present some examples to compare the convergence rate of iterative processes due to Picard, Mann, Ishikawa, Noor, Agarwal et al. and Sahu and Petrusel.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Reference18 articles.

1. Hussain N, Rafiq A, Damjanović B, Lazovic R: On rate of convergence of various iterative processes. Fixed Point Theory Appl. 2011., 2011: Article ID 45

2. Hussain N, Chugh R, Kumar V, Rafiq A: On the rate of convergence of Kirk type iterative processes. J. Appl. Math. 2012., 2012: Article ID 526503

3. Hussain N, Rafiq A, Ciric LB, Al-Mezel S: Almost stability of the Mann type iteration method with error term involving strictly hemicontractive mappings in smooth Banach spaces. J. Inequal. Appl. 2012., 2012: Article ID 207

4. Hussain N, Rafiq A, Ciric LB: Stability of the Ishikawa iteration process with errors for two strictly hemicontractive operators in Banach spaces. Fixed Point Theory Appl. 2012., 2012: Article ID 160

5. Khan SH, Rafiq A, Hussain N: A three-step iterative process for solving nonlinear phi-strongly accretive operator equations in Banach spaces. Fixed Point Theory Appl. 2012., 2012: Article ID 149

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