A simple proof of the Damascus inequality

S. I. Kalinin, L. V. Pankratova

Department of Fundamental Mathematics, Vyatka State University, Kirov, Russia

Abstract: The article is devoted to the presentation of a new proof of the so-called Damascus inequality, formulated in 2016 by Fozi M. Dannan, Professor of the Department of Fundamental Sciences of the Arab International University (Damascus, Syria). The presented proof is based on the apparatus of applying the derivative of a function of one real variable, as well as elementary methods of estimating quantities, including the use of classical inequalities. An important element of the proof is the appeal to the properties of a strictly $GA$-convex (-concave) function on an interval. The implementation of this method of proof also made it possible to describe the conditions for achieving equality in the inequality under consideration.

Keywords: Damascus inequality, geometric mean, logarithmic mean, $GA$-convex (-concave) function.

UDC: 517.165

MSC: 26D07

Received: 02.12.2024
Revised: 01.05.2025
Accepted: 08.05.2025

Language: English

DOI: 10.15393/j3.art.2025.17230