Korovkin Second Theorem via -Statistical -Summability

Abstract and Applied Analysis - Tập 2013 - Trang 1-6 - 2013
M. ‎Mursaleen1, Adem Kılıçman2
1Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
2Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Tóm tắt

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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Abstract and Applied Analysis

Tập 2013

1-6

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