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Korovkin second theorem via B-statistical A-summability


Mursaleen, Mohammad and Kilicman, Adem (2013) Korovkin second theorem via B-statistical A-summability. Abstract and Applied Analysis, 2013. art. no. 598963. pp. 1-6. ISSN 1085-3375; ESSN: 1687-0409


Korovkin type approximation theorems are useful tools to check whether a given sequence (Ln) n ≥ 1 of positive linear operators on C [ 0,1 ] of all continuous functions on the real interval [ 0,1 ] is an approximation process. That is, these theorems exhibit a variety of test functions which assure that the approximation property holds on the whole space if it holds for them. Such a property was discovered by Korovkin in 1953 for the functions 1, x, and x 2 in the space C [ 0,1 ] as well as for the functions 1, cos, and sin in the space of all continuous 2 π -periodic functions on the real line. In this paper, we use the notion of B -statistical A -summability to prove the Korovkin second approximation theorem. We also study the rate of B -statistical A -summability of a sequence of positive linear operators defined from C 2 π (ℝ) into C 2 π (ℝ).

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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.1155/2013/598963
Publisher: Hindawi Publishing Corporation
Keywords: Statistical summability; Korovkin
Depositing User: Umikalthom Abdullah
Date Deposited: 02 Jul 2014 00:20
Last Modified: 20 Oct 2017 04:19
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1155/2013/598963
URI: http://psasir.upm.edu.my/id/eprint/30126
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