Schur Convexity and Inequalities for a Multivariate Symmetric Function

Abstract

In the article, we provide the Schur, Schur multiplicative, and Schur harmonic convexities properties for the symmetry function Fnx,r=Fnx1,x2,⋯,xn;r=∏1≤i1<i2<⋯<ir≤n ∑j=1r xij/1−xij1/r on 0,1n and find several new analytical inequalities by use of the majorization theory, where x=x1,⋯,xn∈0,1n, r=1,2,⋯,n and i1,i2,⋯,in are positive integers.