Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2013 (2013), Article ID 598963, 6 pages.
Korovkin Second Theorem via -Statistical -Summability
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 .
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 598963, 6 pages.
First available in Project Euclid: 18 April 2013
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Mursaleen, M.; Kiliçman, A. Korovkin Second Theorem via $B$ -Statistical $A$ -Summability. Abstr. Appl. Anal. 2013 (2013), Article ID 598963, 6 pages. doi:10.1155/2013/598963. https://projecteuclid.org/euclid.aaa/1366306746