Refinements of Jensen's inequality

Refinements of Pinsker's inequality

Let V and D denote, respectively, total variation and divergence. We study lower bounds of D with V fixed. The theoretically best (i.e. largest) lower bound determines a function L = L(V ), Vajda’s tight lower bound, cf. Vajda, [?]. The main result is an exact parametrization of L. This leads to Taylor polynomials which are lower bounds for L, and thereby extensions of the classical Pinsker ine...

Refinements of Generalized Hölder’s Inequality

In this paper, we present some refinements of a generalized Hölder’s inequality, which is due to Vasić and Pečarić. Mathematics subject classification (2010): Primary 26D15; Secondary 26D10.

An Extension of Chebyshevs Inequality and Its Connection with Jensens Inequality

The aim of this paper is to show that Jensen’s Inequality and an extension of Chebyshev’s Inequality complement one another, so that they both can be formulated in a pairing form, including a second inequality, that provides an estimate for the classical one. 1. Introduction The well known fact that the derivative and the integral are inverse each other has a lot of interesting consequences, on...

Refinements of Kantorovich Inequality for Hermitian Matrices

New refinements of generalized Aczél inequality

*Correspondence: [email protected] 1College of Science and Technology, North China Electric Power University, Baoding, Hebei 071051, P.R. China Full list of author information is available at the end of the article Abstract In this article, we present several new refinements of the generalized Aczél inequality. As an application, an integral type of the generalized Aczél-Vasić-Pečarić ine...