文章基本信息

标题：Strong Convergence of a New Three Step Iterative Scheme in Banach Spaces
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作者：Renu Chugh ; Vivek Kumar ; Sanjay Kumar 等
期刊名称：American Journal of Computational Mathematics
印刷版ISSN：2161-1203
电子版ISSN：2161-1211
出版年度：2012
卷号：2
期号：4
页码：345-357
DOI：10.4236/ajcm.2012.24048
出版社：Scientific Research Publishing
摘要：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.
关键词：Fixed Point; Various Iterative Schemes; Rate of Convergence