Schur Power Convexity of the Daróczy 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.

Necessary and Sufficient Conditions for Schur Geometrical Convexity of the Four-Parameter Homogeneous Means

and Applied Analysis 3 where L x, y , I x, y denote logarithmic mean and identric exponential mean, respectively, G a, b √ ab. The Schur convexity of Sp,q a, b and Gp,q a, b on 0,∞ × 0,∞ with respect to a, b was investigated by Qi et al. 4 , Shi et al. 5 , Li and Shi 6 , and Chu and Zhang 7 . Until now, they have been perfectly solved by Chu and Zhang 7 , Wang and Zhang 8 , respectively. Recent...

Schur–harmonic Convexity for Differences of Some Special Means in Two Variables

In the paper, the authors find Schur-harmonic convexity of linear combinations of differences between some means such as the arithmetic, geometric, harmonic, and root-square means, and establish some inequalities related to these means and differences. Mathematics subject classification (2010): Primary 26E60; Secondary 26B25, 26D20.

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.

Schur Convexity of Generalized Heronian Means Involving Two Parameters