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2019 Log-concavity of Hölder means and an application to geometric inequalities
Aurel I. Stan, Sergio D. Zapeta-Tzul
Involve 12(4): 671-686 (2019). DOI: 10.2140/involve.2019.12.671

Abstract

The log-concavity of the Hölder mean of two numbers, as a function of its index, is presented first. The notion of α-cevian of a triangle is introduced next, for any real number α. We use this property of the Hölder mean to find the smallest index p(α) such that the length of an α-cevian of a triangle is less than or equal to the p(α)-Hölder mean of the lengths of the two sides of the triangle that are adjacent to that cevian.

Citation

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Aurel I. Stan. Sergio D. Zapeta-Tzul. "Log-concavity of Hölder means and an application to geometric inequalities." Involve 12 (4) 671 - 686, 2019. https://doi.org/10.2140/involve.2019.12.671

Information

Received: 23 May 2018; Revised: 9 November 2018; Accepted: 15 November 2018; Published: 2019
First available in Project Euclid: 30 May 2019

zbMATH: 07072546
MathSciNet: MR3941605
Digital Object Identifier: 10.2140/involve.2019.12.671

Subjects:
Primary: 26A06, 26D99

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 4 • 2019
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