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2013 Korovkin Second Theorem via B -Statistical A -Summability
M. Mursaleen, A. Kiliçman
Abstr. Appl. Anal. 2013: 1-6 (2013). DOI: 10.1155/2013/598963


Korovkin type approximation theorems are useful tools to check whether a given sequence ( L n ) 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 ( ) into C 2 π ( ) .


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M. Mursaleen. A. Kiliçman. "Korovkin Second Theorem via B -Statistical A -Summability." Abstr. Appl. Anal. 2013 1 - 6, 2013.


Published: 2013
First available in Project Euclid: 18 April 2013

zbMATH: 06161356
MathSciNet: MR3034945
Digital Object Identifier: 10.1155/2013/598963

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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