Schur m-Power Convexity of a Class of Multiplicatively Convex Functions and Applications - Wen Wang; Shiguo Yang (Abstract and Applied Analysis)
We investigate the conditions under which the symmetric functions Fn,k(x,r)=∏1≤i1<i2<⋯<ik≤n ‍f(∑j=1k‍xijr)1/r,  k=1,2,…,n, are Schur m-power convex for x∈R++n and r>0. As a consequence, we prove that these functions are Schur geometrically convex and Schur harmonically convex, which generalizes some known results. By applying the theory of majorization, several inequalities involving the pth power mean and the arithmetic, the geometric, or the harmonic means are presented.