The Schur Multiplicative and Harmonic Convexities for Three Classes of Symmetric Functions

Abstract

We investigate the Schur harmonic convexity for two classes of symmetric functions and the Schur multiplicative convexity for a class of symmetric functions by using a new method and generalizing previous result. As applications, we establish some inequalities by use of the theory of majorization, in particular, and we give some new geometric inequalities in the n-dimensional space.