Schur-Convexity for Elementary Symmetric Composite Functions and Their Inverse Problems and Applications

Abstract

This paper investigates the Schur-convexity, Schur-geometric convexity, and Schur-harmonic convexity for the elementary symmetric composite function and its dual form. The inverse problems are also considered. New inequalities on special means are established by using the theory of majorization.

Keywords

• symmetric function
• Schur-convexity
• inequality
• special means