Korovkin Second Theorem via B‐Statistical A‐Summability

M. Mursaleen and A. Kiliçman

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: 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 x2 in the space C[0,1] as well as for the functions 1, cos, and sin in the space of all continuous 2π‐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 C2π(ℝ) into C2π(ℝ).

Date: 2013
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https://doi.org/10.1155/2013/598963

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:598963

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