Involve: A Journal of Mathematics
- Volume 12, Number 4 (2019), 671-686.
Log-concavity of Hölder means and an application to geometric inequalities
The log-concavity of the Hölder mean of two numbers, as a function of its index, is presented first. The notion of -cevian of a triangle is introduced next, for any real number . We use this property of the Hölder mean to find the smallest index such that the length of an -cevian of a triangle is less than or equal to the -Hölder mean of the lengths of the two sides of the triangle that are adjacent to that cevian.
Involve, Volume 12, Number 4 (2019), 671-686.
Received: 23 May 2018
Revised: 9 November 2018
Accepted: 15 November 2018
First available in Project Euclid: 30 May 2019
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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