SCHUR POWER CONVEXITY OF GINI MEANS

Schur-convexity and Schur-geometrically concavity of Gini means

The monotonicity and the Schur-convexity with parameters (s, t) in R2 for fixed (x, y) and the Schur-convexity and the Schur-geometrically convexity with variables (x, y) in R++ for fixed (s, t) of Gini mean G(r, s;x, y) are discussed. Some new inequalities are obtained.

Schur Power Convexity of the Daróczy Means

In this paper, the Schur convexity is generalized to Schur f -convexity, which contains the Schur geometrical convexity, harmonic convexity and so on. When f : R+ →R is defined by f (x) = (xm−1)/m if m = 0 and f (x) = lnx if m = 0 , the necessary and sufficient conditions for f -convexity (is called Schur m -power convexity) of Daróczy means are given, which improve, generalize and unify Shi et...

Logarithmic Convexity of Gini Means

where x and y are positive variables and r and s are real variables. They are also called sum mean values. There has been a lot of literature such as [3, 4, 5, 6, 9, 10, 11, 12, 13, 19, 20, 21] and the related references therein about inequalities and properties of Gini means. The aim of this paper is to prove the monotonicity and logarithmic convexity of Gini means G(r, s;x, y) and related fun...

Schur Convexity of Generalized Heronian Means Involving Two Parameters

Schur-convexity, Schur-geometric and Schur-harmonic convexity for a composite function of complete symmetric function

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 and Schur-harmonic convexity for a composite function of the complete symmetric function.