Some best possible integral estimates involving Bernoulli polynomials (Q1984248)
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scientific article; zbMATH DE number 7394762
| Language | Label | Description | Also known as |
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| English | Some best possible integral estimates involving Bernoulli polynomials |
scientific article; zbMATH DE number 7394762 |
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Some best possible integral estimates involving Bernoulli polynomials (English)
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13 September 2021
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The authors of the paper under review are inspired by [``Problem 4615'', Crux Math. 47, No. 2, 97 (2021)], proposed by \textit{A. Garcia}. The authors discuss some new, best possible, integral estimates involving the \(L^{2}\)-norm of the second derivative of smooth periodic as well as nonperiodic functions. In support of their arguments they make use of Wirtinger-type inequalities for integrals, Fourier series of \(1\)-periodic functions, Parseval's formula, the fourth Bernoulli polynomial \(B4\), and the Cauchy-Schwarz inequality.
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integral estimates
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Bernoulli polynomials
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\(L^2\)-norm
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second derivatives
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