This paper is twofold. In the first part, we derive an improvement of the Rényi Entropy Power Inequality (EPI) recently obtained by Bobkov and Marsiglietti [10]. The proof largely follows Lieb’s [22] approach of employing Young’s inequality. In the second part, we prove a reverse Rényi EPI, that verifies a conjecture proposed in [4, 23] in two cases. Connections with various p-th mean bodies in...

In this short note, we present a refinement of the logarithmic-geometric mean inequality. As an application of our result, we obtain an operator inequality associated with geometric and logarithmic means.

Convex solutions to the power-of-mean curvature flow, conformally invariant inequalities and regularity results in some applications of optimal transportation Shibing Chen Doctor of Philosophy Graduate Department of Mathematics University of Toronto 2012 In this thesis we study three different problems: convex ancient solutions to the power-ofmean curvature flow; Sharp inequalities; regularity ...

Abstract. Arithmetic, geometric and harmonic means are the three classical means famous in the literature. Another mean such as square-root mean is also known. In this paper, we have constructed divergence measures based on nonnegative differences among these means, and established an interesting inequality by use of properties of Csiszár’s f-divergence. An improvement over this inequality is a...

Consider an income distribution among households of the same size and suppose that the individuals, equally needy from the point of view of an ethical observer, are treated unfairly within each household. We look for conditions under which welfare and inequality quasi-orders are preserved from the household level at the individual one. A necessary and sufficient condition for the Generalized Lo...