Korovkin Second Theorem via -Statistical -Summability

M. Mursaleen and A. Kiliçman

Abstract and Applied Analysis, 2013, vol. 2013, 1-6

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 .

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:598963

DOI: 10.1155/2013/598963

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