Matrix versions of Young's inequality

A Note on Matrix Versions of Kantorovich–type Inequality

Some new matrix versions of Kantorovich-Type inequalities for Hermitian matrix are proposed in this paper. We consider what happens to these inequalities when the positive definite matrix is allowed to be positive semidefinite singular or indefinite.

New versions of Suen's correlation inequality

1. Introduction Suen 8] found a remarkable correlation inequality, giving estimates for the probability that a collection of dependent random indicator variables vanish simultaneously, or in other words, for the probability that none of a collection of dependent events occurs. The present author 4, 3] has found similar inequalities for a much more restricted situation; when applicable, these in...

Multidimensional Lower Density Versions of Plünnecke's Inequality

We investigate the lower asymptotic density of sumsets in N2 by proving certain Plünnecke type inequalities for various notions of lower density in N2. More specifically, we introduce a notion of lower tableaux density in N2 which involves averaging over convex tableaux-shaped regions in N2 which contain the origin. This generalizes the well known Plünnecke type inequality for the lower asympto...

Stability of some versions of the Prékopa-Leindler inequality

Two consequences of the stability version of the one dimensional Prékopa-Leindler inequality are presented. One is the stability version of the Blaschke-Santaló inequality, and the other is a stability version of the Prékopa-Leindler inequality for even functions in higher dimensions, where a recent stability version of the Brunn-Minkowski inequality is also used in an essential way. 1 The prob...

Cyclic Refinements of the Different Versions of Operator Jensen's Inequality