We give three proofs of a functional inequality for the standard Gaussian measure originally due to William Beckner. The first uses the central limit theorem and a tensorial property of the inequality. The second uses the Ornstein-Uhlenbeck semigroup, and the third uses the heat semigroup. These latter two proofs yield a more general inequality than the one Beckner originally proved. We then ge...

This paper contributes to the ongoing debate about economic inequality in India during the post-reform period. We analyze consumption inequality through the hitherto neglected lens of nonfood expenditure. Using household level consumption expenditure data from the quinquennial “thick” rounds of the NSS, we show that inequality within food and non-food groups has declined, even as overall expend...

For bounded non-negative operators A and B, Furuta showed 0 ≤ A ≤ B implies A r 2BA r 2 ≤ (A r 2BA r 2 ) s+r t+r (0 ≤ r, 0 ≤ s ≤ t). We will extend this as follows: 0 ≤ A ≤ B ! λ C (0 < λ < 1) implies A r 2 (λB + (1− λ)C)A r 2 ≤ {A r 2 (λB + (1 − λ)C)A r 2 } s+r t+r , where B ! λ C is a harmonic mean of B and C. The idea of the proof comes from Jensen’s inequality for an operator convex functio...

Focus must be shifted from income inequality to economic inequality because of the presence of causal influences on individual well-being and freedom that are economic in nature but cannot be expounded by simple statistics of incomes and commodity holdings. Attention must be given to heterogeneous magnitudes. Moreover, there is a need for the derivation of partial orderings based on explicit or...

The rapid increase of wealth inequality in the past few decades is one of the most disturbing social and economic issues of our time. Studying its origin and underlying mechanisms is essential for policy aiming to control and even reverse this trend. In that context, controlling the distribution of income, using income tax or other macroeconomic policy instruments, is generally perceived as eff...

Previous systematic reviews of population-level tobacco control interventions and their effects on smoking inequality by socioeconomic factors concluded that tobacco taxation reduce smoking inequality by income (although this is not consistent for other socioeconomic factors, such as education). Inconsistent results have been reported for socioeconomic differences, especially for other tobacco ...

The study examined the linkages between inequality in household expenditure components and total inequality and poverty in Ghana. Using micro data from the sixth round of the Ghana Living Standards Survey conducted in 2012/2013, marginal effects and elasticities were computed for both within-and between-component analysis. The results suggest that, in general, reducing within-component inequali...

Let $C$ be a nonempty closed convex subset of a real Banach space $E$, let $B: C rightarrow E $ be a nonlinear map, and let  $u, v$ be  positive numbers. In this paper, we show  that  the generalized variational inequality $V I (C, B)$ is singleton for $(u, v)$-cocoercive mappings under appropriate assumptions on Banach spaces. The main results are extensions of the Saeidi's Propositions for fi...

In this paper we find a characterization type result for (η1,η2)-convex functions. The Fejér integral inequality related to (η1,η2)-convex functions is obtained as a generalization of Fejér inequality related to the preinvex and η-convex functions. Also some Fejér trapezoid and midpoint type inequalities are given in the case that the absolute value of the derivative of considered function is (...