Strong Convergence of a New Three Step Iterative Scheme in Banach Spaces

Renu Chugh, Vivek Kumar, Sanjay Kumar

Department of Mathematics, Maharshi Dayanand University, Rohtak, India.

DOI: 10.4236/ajcm.2012.24048                

Abstract

In this paper, we suggest a new type of three step iterative scheme called the CR iterative scheme and study the strong convergence of this iterative scheme for a certain class of quasi-contractive operators in Banach spaces. We show that for the aforementioned class of operators, the CR iterative scheme is equivalent to and faster than Picard, Mann, Ishikawa, Agarwal et al., Noor and SP iterative schemes. Moreover, we also present various numerical examples using computer programming in C++ for the CR iterative scheme to compare it with the other above mentioned iterative schemes. Our results show that as far as the rate of convergence is concerned 1) for increasing functions the CR iterative scheme is best, while for decreasing functions the SP iterative scheme is best; 2) CR iterative scheme is best for a certain class of quasi-contractive operators.

Keywords

Fixed Point; Various Iterative Schemes; Rate of Convergence

Conflicts of Interest

The authors declare no conflicts of interest.

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