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

Chugh, Renu and Kumar, Vivek and Kumar, Sanjay (2012) Strong Convergence of a New Three Step Iterative Scheme in Banach Spaces. American Journal of Computational Mathematics, 02 (04). pp. 345-357. ISSN 2161-1203

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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.

Item Type: Article
Subjects: AP Academic Press > Mathematical Science
Depositing User: Unnamed user with email support@apacademicpress.com
Date Deposited: 20 Jun 2023 09:50
Last Modified: 19 Sep 2024 09:10
URI: http://info.openarchivespress.com/id/eprint/1601

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