Korovkin second theorem via B-statistical A-summability
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30126/1/30126.pdf http://psasir.upm.edu.my/id/eprint/30126/ http://www.hindawi.com/journals/aaa/2013/598963/ |
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| Summary: | 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 x 2 in the space C [ 0,1 ] as well as for the functions 1, cos, and sin in the space of all continuous 2 π -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 C 2 π (ℝ) into C 2 π (ℝ). |
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