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Korovkin Second Theorem via -Statistical -Summability

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  • M. Mursaleen
  • A. Kiliçman

Abstract

Korovkin type approximation theorems are useful tools to check whether a given sequence of positive linear operators on of all continuous functions on the real interval 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, , and in the space as well as for the functions 1, cos, and sin in the space of all continuous 2 -periodic functions on the real line. In this paper, we use the notion of -statistical -summability to prove the Korovkin second approximation theorem. We also study the rate of -statistical -summability of a sequence of positive linear operators defined from into .

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  • M. Mursaleen & A. Kiliçman, 2013. "Korovkin Second Theorem via -Statistical -Summability," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, February.
    • Handle: RePEc:hin:jnlaaa:598963
    DOI: 10.1155/2013/598963
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    Cited by:

    1. Mursaleen, M. & Khan, Faisal & Khan, Asif, 2014. "Statistical approximation for new positive linear operators of Lagrange type," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 548-558.

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