On the Jackson theorem for periodic functions in metric spaces with integral metric. II (Q1760017)
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scientific article; zbMATH DE number 6110059
| Language | Label | Description | Also known as |
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| English | On the Jackson theorem for periodic functions in metric spaces with integral metric. II |
scientific article; zbMATH DE number 6110059 |
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On the Jackson theorem for periodic functions in metric spaces with integral metric. II (English)
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23 November 2012
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The paper is a continuation of the author's previous paper, [Ukr. Math. J. 52, No. 1, 133--147 (2000); translation from Ukr. Mat. Zh. 52, No. 1, 122--133 (2000; Zbl 0987.42002)] and extends the conditions for the validity of Jackson's theorem. It is proved that the direct Jackson theorem is true if and only if the lower dilation index of a function of the type of modulus of continuity is not equal to zero in the space of periodic functions.
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Jackson theorem
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approximation
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trigonometric polynomials
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dilation function
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