Involve: A Journal of Mathematics

• Involve
• Volume 12, Number 4 (2019), 671-686.

Log-concavity of Hölder means and an application to geometric inequalities

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.

Article information

Source
Involve, Volume 12, Number 4 (2019), 671-686.

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

Permanent link to this document
https://projecteuclid.org/euclid.involve/1559181659

Digital Object Identifier
doi:10.2140/involve.2019.12.671

Mathematical Reviews number (MathSciNet)
MR3941605

Zentralblatt MATH identifier
07072546

Citation

Stan, Aurel I.; Zapeta-Tzul, Sergio D. Log-concavity of Hölder means and an application to geometric inequalities. Involve 12 (2019), no. 4, 671--686. doi:10.2140/involve.2019.12.671. https://projecteuclid.org/euclid.involve/1559181659

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