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2004•Izvestiya MathematicsRequires access

Inequalities for derivatives of rational functions on several intervals

Alexey Lukashov

Open publisher page 32 citations

Abstract

We describe a solution of the problem of finding rational trigonometric functions with fixed denominator that deviate least from zero on several subintervals of the period. The resulting representation is used to prove inequalities that estimate the derivatives of rational trigonometric and algebraic functions with fixed denominator in terms of their values on several intervals. Particular cases of these inequalities include the well-known inequalities of Videnskii, Rusak, Totik and others.

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What this paper is about

We describe a solution of the problem of finding rational trigonometric functions with fixed denominator that deviate least from zero on several subintervals of the period. The resulting representation is used to prove inequalities that estimate the derivatives of rational trigonometric and algebraic functions with fixed denominator in terms of their values on several intervals. Particular cases of these inequalities include the well-known inequalities of Videnskii, Rusak, Totik and others.

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Available abstract

We describe a solution of the problem of finding rational trigonometric functions with fixed denominator that deviate least from zero on several subintervals of the period. The resulting representation is used to prove inequalities that estimate the derivatives of rational trigonometric and algebraic functions with fixed denominator in terms of their values on several intervals. Particular cases of these inequalities include the well-known inequalities of Videnskii, Rusak, Totik and others.

Key concepts: Mathematics, Inequality, Mathematical economics, Applied mathematics, Pure mathematics, Calculus (dental), Econometrics, Mathematical analysis

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