On a trigonometric inequality of Szegő and Schweitzer
type: Item
instance of: scholarly article
title: On a trigonometric inequality of Szegő and Schweitzer
zbMATH Open document ID: 1486.26026
author: Horst Alzer
author: Man Kam Kwong
published in: Rocky Mountain Journal of Mathematics
publication date: 2021-09-10T00:00:00Z
review text: Inequalities for trigonometric polynomials have applications in geometric function theory and other fields. The present study has been motivated by \textit{R. Askey} and \textit{J. Fitch} [Publ. Fac. Électrotech. Univ. Belgrade, Sér. Math. Phys. 381--409, 131--134 (1972; Zbl 0254.42001)]. This study proves that the inequality \[ \sum_{\begin{array}{c} k=1 \\ k~odd \end{array} }^{n} (n+1-k)(n+2-k)k \sin kx \geq 0,\] for \(n\in \mathbb{N};\) \(0 \leq x \leq \pi\) and \[ \sum_{\begin{array}{c} k=1 \\ k~even \end{array} }^{n} (n+1-k)(n+2-k)k \sin kx \geq 0,\] for \(2 \leq n\in \mathbb{N};\) \(0 \leq x \leq \frac{1}{2}\) arccos \(-\frac{5}{6}.\) Moreover, the authors use the above inequalities to obtain two one-parameter classes of absolutely monotonic functions and show that these functions satisfy a certain functional inequality, too.
Mathematics Subject Classification ID: 26D05
zbMATH DE Number: 7393772
zbMATH Keywords: sine polynomials, inequalities, absolutely monotonic
reviewed by: Praveen Agarwal
MaRDI profile type: Publication
cites work: Q4052481
cites work: Q5669260
cites work: Signs of Derivatives and Analytic Behavior
cites work: Inequalities for Trigonometric Sums
cites work: Q3473576
cites work: Q4861743
cites work: The partial sums of second order of the geometric series
cites work: Power series with multiply monotonic sequences of coefficients
cites work: Q5616564
cites work: Q5846853
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description: scientific article; zbMATH DE number 7393772