Logarithmic Convexity of Gini Means

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-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.

Research Article On Logarithmic Convexity for Differences of Power Means

Inequalities among Differences of Gini Means and Divergence Measures

In 1938, Gini [3] studied a mean having two parameters. Later, many authors studied properties of this mean. In particular, it contains the famous means as harmonic, geometric, arithmetic, etc. Here we considered a sequence of inequalities arising due to particular values of each parameter of Gini’s mean. This sequence generates many nonnegative differences. Not all of them are convex. We have ...

A new index for measuring aging inequality: An application to Asian countries

Although the Gini coefficient is an ideal measure of income inequality, it may be applied to measure the aging inequality in a society. In this paper, an attempt has been made to develop alternative measures of aging inequality based on the Gini index. The study uses the secondary population data of Asian countries collected from the international data base, US census Bureau. From the analysis ...