Sharp inequalities between mean quantities via convexity and applications

Abstract

The aim of the present paper is to provide a completely new method that allows us to derive the best possible bounds for one-term refinements and reverses of inequalities between mean quantities. These results cover and refine almost all inequalities in the literature. Applications to inequalities for matrix means, the traces and determinants of matrices, as well as inequalities for unitarily invariant norms and numerical radius norms, are also discussed.