Related papers: Entropy-power inequality for weighted entropy

We give an overview about the power product expansion of the exponential series and derive some q-analogs

The main purpose of this article is to study estimates for the Tsallis relative operator entropy, by the use of Hermite-Hadamard inequality. Thus, we obtain alternative bounds for the Tsallis relative operator entropy. In the process to…

We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by improvements of Young's inequality. We also give a generalized Han's inequality.

In this note we prove a weighted version of the Khintchine inequalities.

A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.

In this article we derive some polynomial inequalities for Mertens functions.

We survey several notions of entropy related to a compact manifold of negative curvature, some relations between them, and the rigidity problems.

Following [1], the aim of this paper is to analyze the relative weighted entropy involving the central moments weight functions. We compare the standard relative entropy with the weighted case in two particular forms of Gaussian…

We derive a relative entropy inequality for capillary compressible fluids with density dependent viscosity. Applications in the context of weak-strong uniqueness analysis, pressureless fluids and high-Mach number flows are presented.

In this paper, a method of measuring the entropy is presented. Problems related to the entropy and the heat are also discussed.

This paper is twofold. In the first part, we present a refinement of the R\'enyi Entropy Power Inequality (EPI) recently obtained in \cite{BM16}. The proof largely follows the approach in \cite{DCT91} of employing Young's convolution…

Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.

In this article we discuss a generalized Wirtinger inequality.

We establish some new generalizations of Erd\H{o}s-Mordell inequality by adding weights to its terms. Using these generalizations, we derived strengthened versions of the original Erd\H{o}s-Mordell inequality. We also found two other…

A lower bound on the R\'enyi differential entropy of a sum of independent random vectors is demonstrated in terms of rearrangements. For the special case of Boltzmann-Shannon entropy, this lower bound is better than that given by the…

We prove in this note one weight norm inequalities for some positive Bergman-type operators.

Deformed logarithms and their inverse functions, the deformed exponentials, are important tools in the theory of non-additive entropies and non-extensive statistical mechanics. We formulate and prove counterparts of Golden-Thompson's trace…

We prove an inequality for the entropy numbers in terms of nonlinear Kolmogorov's widths. This inequality is in a spirit of known inequalities of this type and it is adjusted to the form convenient in applications for $m$-term…

We review the plethora of uncertainty relations that appear in quantum mechanics and their nuances. We present both foundational applications, e.g. in understanding and defining complementarity, and practical applications, e.g. in quantum…

We give a q-analogue of Gauss' divisibility theorem