Inequalities for majorizing analytic functions and their applications to rational trigonometric functions and polynomials

A. V. Olesov

Maritime State University named after G. I. Nevelskoi

Abstract: New inequalities are established for analytic functions satisfying Meiman's majorization conditions. Estimates for values of and differential inequalities involving rational trigonometric functions with an integer majorant on an interval of length less than the period and with prescribed poles which are symmetrically positioned relative to the real axis, as well as differential inequalities for trigonometric polynomials in some classes, are given as applications. These results improve several theorems due to Meiman, Genchev, Smirnov and Rusak.
Bibliography: 27 titles.

Keywords: majorizing analytic functions, entire functions of exponential type, rational trigonometric functions, polynomials, Bernstein-type inequalities.

UDC: 517.54+517.535

MSC: 30C10, 30C80

Received: 31.05.2012 and 19.07.2014

DOI: 10.4213/sm8146

 English version: Sbornik: Mathematics, 2014, 205:10, 1413–1441

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