Schur Convexity for a Class of Symmetric Functions

The Schur-convex function was introduced by I. Schur in 1923, and it has many important applications in analytic inequalities, generalized means, statistics experiment, chart and matrix, combinatorial optimization, reliability, information security, random sorting, etc. So it is important that Schur-convexity for symmetric functions of several variables is researched. In this paper, Guan’s symmetric function was improved, and a class of symmetric functions were derived. By so-called Schur’s condition, Schur-convexity and Schur-geometric convexity and Schur-harmonic convexity are studied for a class of symmetric functions.