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October 2021 A unified extension of some classical Hilbert-type inequalities and applications
Minghui You
Rocky Mountain J. Math. 51(5): 1865-1877 (October 2021). DOI: 10.1216/rmj.2021.51.1865

Abstract

We first establish a new Hilbert-type inequality involving the kernel including both the homogeneous and the nonhomogeneous cases, and the constant factor of the newly obtained inequality is proved to be the best possible. Additionally, by means of Leibniz integral rule and the rational fraction expansion of trigonometric functions, we derive the representation of the best possible constant factor by the logarithmic function and the higher derivative of trigonometric functions, which leads to a few special and interesting inequalities. Furthermore, We also demonstrate that our newly obtained inequality is a unified generalization of some classical Hilbert-type inequalities.

Citation

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Minghui You. "A unified extension of some classical Hilbert-type inequalities and applications." Rocky Mountain J. Math. 51 (5) 1865 - 1877, October 2021. https://doi.org/10.1216/rmj.2021.51.1865

Information

Received: 12 October 2020; Revised: 27 December 2020; Accepted: 13 January 2021; Published: October 2021
First available in Project Euclid: 17 February 2022

Digital Object Identifier: 10.1216/rmj.2021.51.1865

Subjects:
Primary: 26D10 , 26D15
Secondary: 41A17 , 47B38

Keywords: Hilbert-type inequality , Leibniz integral rule , rational fraction expansion , unified extension

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 5 • October 2021
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