Inequalities for trigonometric polynomials and some integral means. (English) Zbl 0977.41006
The authors obtain a number of inequalities associated with the Laplacian for trigonometric polynomials and use them to investigate approximation by trigonometric polynomials in higher dimensions. Also an interesting result concerning the classical Jackson operator is obtained. They show that the approximation error of a function by Jackson polynomials is equivalent to a \(K\)-functional defined by the Laplacian.
Reviewer: S.M.Mazhar (Kuwait)
MSC:
| 41A17 | Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities) |
| 42A10 | Trigonometric approximation |
Keywords:
Bernstein inequality; Jackson inequality; Laplacian \(K\)-functional; \(K\)-functional; Jackson operatorReferences:
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