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

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.

Schur-Convexity of a Class of Elementary Symmetric Composite Functions

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.

Extensions of Hermite–Hadamard inequalities for harmonically convex functions via generalized fractional integrals

In the paper, the authors establish some new Hermite–Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite–Hadamard inequality for harmonically convex functions via generalized fractional integrals without using the harmonic convexity property for the functions. The results offered here are the refinements of the existing results for harmonically convex functions.

Generalizations of the Ostrowski type inequalities using different types of convexity

In this paper we establish some Ostrowski type inequalities using some classes of convex functions. We will use the following types of convexity: (α, m, h)-convexity, log-convexity and the Arithmetic-Harmonic convexity(AHconvexity).

Schur convexity of mixed mean of n variables involving three parameters

In this paper, we discuss the Schur convexity, the Schur geometric convexity and Schur harmonic convexity of the mixed mean of n variables involving three parameters. As an application, we have established some inequalities of the Ky Fan type related to the mixed mean of n variables, and the lower bound inequality of Gini mean for n variables is given.

Schur-harmonic convexity related to co-ordinated harmonically convex functions in plane

In this paper, we investigate Schur-harmonic convexity of some functions which are obtained from the co-ordinated harmonically convex functions on a square in a plane.

On approximately harmonic h-convex functions depending on a given function

A new class of harmonic convex function depending on given functions which is called as ?approximately harmonic h-convex functions? is introduced. With the discussion of special cases it is shown that this class unifies other classes of approximately harmonic h-convex function. Some associated integral inequalities with these new classes of harmonic convexity are also obtained. Several special cases of the main results are also discussed.

The Schur Multiplicative and Harmonic Convexities for Three Classes of Symmetric Functions

We investigate the Schur harmonic convexity for two classes of symmetric functions and the Schur multiplicative convexity for a class of symmetric functions by using a new method and generalizing previous result. As applications, we establish some inequalities by use of the theory of majorization, in particular, and we give some new geometric inequalities in the n-dimensional space.