A Class of Schur Convex Functions and Several Geometric Inequalities

Abstract

Schur convexity, Schur geometrical convexity and Schur harmonic convexity of a class of symmetric functions are investigated. As consequences some known inequalities are generalized. In addition, a class of geometric inequalities involving $n$-dimensional simplex in $n$-dimensional Euclidean space $E^n$ and several matrix inequalities are established to show the applications of our results.