We give bounds on the difference between weighted arithmetic mean and geometric mean. These imply refined Young inequalities reverses of inequality. also study some properties Applying newly obtained inequalities, we show results Tsallis divergence, R\'{e}nyi Jeffreys-Tsallis divergence Jensen-Shannon-Tsallis divergence.

Parents play major roles in determining the human capital of children, and thus the income of children when they become adults. Models of investments in children’s human capital posit that these investments are determined by parental resources (financial and human capital) and child endowments within particular market and policy environments. Many empirical studies are consistent with significa...

Let L be a finite distributive lattice and μ : L → R a logsupermodular function. For functions k : L → R let Eμ(k; q) def = ∑ x∈L k(x)μ(x)q ∈ R[q]. We prove for any pair g, h : L → R of monotonely increasing functions, that Eμ(g; q) ·Eμ(h; q) ≪ Eμ(1; q) · Eμ(gh; q), where “≪ ” denotes coefficientwise inequality of real polynomials. The FKG inequality of Fortuin, Kasteleyn and Ginibre (1971) is ...

We examine how aggregate output and income distribution interact with accumulation of intangible capital over time and across individuals. We consider an overlapping generations economy in which managerial skill (intangible capital) is essential for production, and it is acquired by young workers through on-the-job training by old managers. We show that, when young trainees are not committed to...

Several maximal inequalities of Kahane-Khintchine’s type in certain Orlicz spaces are proved. The method relies upon Lévy’s inequality and the technique established in [14] which is obtained by Haagerup-Young-Stechkin’s best possible constants in the classical Khintchine inequalities. Moreover by using Donsker’s invariance principle it is shown that the numerical constant in the inequality dedu...

Many recent studies point to increasing inequality in mortality in the United States over the past 20 years. These studies often use mortality rates in middle and old age. We used poverty level rankings of groups of U.S. counties as a basis for analyzing inequality in mortality for all age groups in 1990, 2000, and 2010. Consistent with previous studies, we found increasing inequality in mortal...

A recent literature on inequality of opportunity offers quantitative tools for comparisons and measurement based on stochastic dominance criteria and traditional inequality indices. In this paper I suggest an additional way of assessing inequality of opportunity with two indices of dissimilarity across distributions. The indices are based on a traditional homogeneity test of multinomial distrib...

OBJECTIVE To achieve universal coverage of reproductive healthcare and drastic reduction in maternal mortality, adequate attention and resources should be given to young women. This study therefore aimed to examine the inequality trends in the use of antenatal care (ANC) services and skilled birth attendance (SBA) within a subgroup of Ghanaian women aged 15-24 years between 2003 and 2014. DES...