(untitled) (Communications in Mathematical Research, 2021)
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.