TL;DR
This paper discusses the Damascus Inequality for three positive numbers with unit product, providing proofs, generalizations, and exploring related open problems and conjectures.
Contribution
It offers multiple proofs of the inequality, extends it to generalizations, and investigates connected unsolved problems and conjectures.
Findings
Multiple proofs of the inequality are presented.
Generalizations of the inequality are proposed.
Several open problems and conjectures are discussed.
Abstract
In 2016 Prof. Fozi M. Dannan from Damascus, Syria proposed an inequality for three positive numbers with unit product. It became widely known but was not proved yet in spite of elementary formulation. We give some proofs for this inequality, a number of its generalizations and some connected unsolved problems and conjectures.
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