The Schur Harmonic Convexity of the Hamy Symmetric Function and Its Applications

Abstract

We prove that the Hamy symmetric function Fn(x,r)=∑1≤i1<i2<⋯<ir≤n(∏j=1rxij)1/r is Schur harmonic convex for x∈R+n. As its applications, some analytic inequalities including the well-known Weierstrass inequalities are obtained.