This article is cited in 1 paper

Applied mathematics

Generalization of Levin–Stechkin inequality

R. N. Miroshin

St. Petersburg State University, Department of Mathematics and Mechanics

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.

UDC: 519.24


Accepted: May 19, 2011