Involve: A Journal of Mathematics

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

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

Aurel I. Stan and Sergio D. Zapeta-Tzul

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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

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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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A06: One-variable calculus 26D99: None of the above, but in this section

Hölder mean log-concavity Jensen inequality triangle cevian


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.

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