相关论文: Refined Young inequality and its application to di…

This work studies the Geometric Jensen-Shannon divergence, based on the notion of geometric mean of probability measures, in the setting of Gaussian measures on an infinite-dimensional Hilbert space. On the set of all Gaussian measures…

In this short note, we give the refined Young inequality with Specht's ratio by only elementary and direct calculations. The obtained inequality is better than one previously shown by the author in 2012. In addition, we give a new property…

This paper extends the asymmetric Kullback-Leibler divergence and symmetric Jensen-Shannon divergence from two probability measures to the case of two sets of probability measures. We establish some fundamental properties of these…

In this paper we have considered two one parametric generalizations. These two generalizations have in articular the well known measures such as: J-divergence, Jensen-Shannon divergence and Arithmetic-Geometric mean divergence. These three…

A considerable amount of literature in the theory of inequality is devoted to the study of Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex…

For a bounded convex domain \Omega in R^N we prove refined Hardy inequalities that involve the Hardy potential corresponding to the distance to the boundary of \Omega, the volume of $\Omega$, as well as a finite number of sharp logarithmic…

In this article, we obtain several new weighted bounds for the numerical radius of a Hilbert space operator. The significance of the obtained results is the way they generalize many existing results in the literature; where certain values…

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 article, we prove several multi-term refinements of Young type inequalities for both real numbers and operators improving several known results. Among other results, we prove \begin{eqnarray*}…

The geometric Jensen--Shannon divergence (G-JSD) gained popularity in machine learning and information sciences thanks to its closed-form expression between Gaussian distributions. In this work, we introduce an alternative definition of the…

We show that Lorentz-Finsler geometry offers a powerful tool in obtaining inequalities. With this aim, we first point out that a series of famous inequalities such as: the (weighted) arithmetic-geometric mean inequality, Acz\'el's,…

In this paper we have considered a single inequality having 11 known divergence measures. This inequality include measures like: Jeffryes-Kullback-Leiber J-divergence, Jensen-Shannon divergence (Burbea-Rao, 1982), arithmetic-geometric mean…

In 1938, Gini 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…

Since its original formulation, Jensen's inequality has played a fundamental role across mathematics, statistics, and machine learning, with its probabilistic version highlighting the nonnegativity of the so-called Jensen's gap, i.e., the…

It is shown that Newton's inequalities and the related Maclaurin's inequalities provide several refinements of the fundamental Arithmetic mean - Geometric mean - Harmonic mean inequality in terms of the means and variance of positive real…

Young's inequality is extended to the context of absolutely continuous measures. Several applications are included.

Firstly, this paper establishes useful forms of the remainder term of Hardy-type inequalities on general domains where the weights are functions of the distance to the boundary. For weakly mean convex domains we use the resulting identities…

Starting with real line number system based on the theory of the Yang's fractional set, the generalized Young inequality is established. By using it some results on the generalized inequality in fractal space are investigated in detail.

In this note, we derive non trivial sharp bounds related to the weighted harmonic-geometric-arithmetic means inequalities, when two out of the three terms are known. As application, we give an explicit bound for the trace of the inverse of…

There are three classical divergence measures exist in the literature on information theory and statistics. These are namely, Jeffryes-Kullback-Leiber J-divergence. Sibson-Burbea-Rao Jensen-Shannon divegernce and Taneja arithemtic-geometric…