Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2013, Issue 1, Pages 18–21 (Mi vspui105)  
This article is cited in 1 scientific paper (total in 1 paper)

Applied mathematics

Generalization of Levin–Stechkin inequality

R. N. Miroshin

St. Petersburg State University, Department of Mathematics and Mechanics
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Abstract: The classical integral Levin-Stechkin inequality on a wider class of integrands is generalized. The integral of the two continuous functions product one of which being unimodal, but not symmetric as in Levin–Stechkin and the second one being convex, is bounded by a sum of products of linear combinations of the first two moments above functions mentioned. The proof uses the moment method and the process of orthogonalization for three functions. The result is illustrated with three examples. Bibliogr. 4.
Keywords: moment method, generalization of Levin–Stechkin inequality, unimodal function, convex function.

Accepted: May 19, 2011
Document Type: Article
UDC: 519.24
Language: Russian
Citation: R. N. Miroshin, “Generalization of Levin–Stechkin inequality”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2013, no. 1, 18–21
Citation in format AMSBIB
\Bibitem{Mir13}
\by R.~N.~Miroshin
\paper Generalization of Levin--Stechkin inequality
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2013
\issue 1
\pages 18--21
\mathnet{http://mi.mathnet.ru/vspui105}
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    • This publication is cited in the following 1 articles:
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    		Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления
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