In this paper, using the properties of Schur-convex function, Schur-geometrically convex function and Schur-harmonically convex function, we provide much simpler proofs of the Schur-convexity, Schur-geometric convexity on and Schur-harmonic convexity on for a composite function of the elementary symmetric functions.
In this paper, we consider a class of geometrically convex function which is called geometrically-arithmetically h-convex function. Some inequalities of Hermite-Hadamard type for geometrically-arithmetically h-convex functions are derived. Several special cases are discussed.
Schur-Convexity of a Class of Elementary Symmetric Composite Functions
