In this paper, we give refinements of the classical Young inequality for scalars and use these to establish refined some type inequalities trace, determinants, norms positive definite matrices.

Jensen’s inequality is sometimes called the king of inequalities [4] because it implies at once the main part of the other classical inequalities (e.g. those by Hölder, Minkowski, Young, and the AGM inequality, etc.). Therefore, it is worth studying it thoroughly and refine it from different points of view. There are numerous refinements of Jensen’s inequality, see e.g. [3-5] and the references...

In this paper, we prove an inequality, which we call " Devroye inequality " , for a large class of non-uniformly hyperbolic dynamical systems (M, f). This class, introduced by L.-S. Young, includes families of piece-wise hyperbolic maps (Lozi-like maps), scattering billiards (e.g., planar Lorentz gas), unimodal and Hénon-like maps. Devroye inequality provides an upper bound for the variance of ...

In this paper, we present some refinements of reverse Young?s inequalities. Among other results, a refinement operator Young inequalities says A?vB + 2?(A?B ? A?B) m??M / A?vB, where 0 < mI A, B MI, = min{v, 1 v} and v [0, 1], extending key result in [J. Math. Anal. Appl. 465 (2018) 267-280] [Linear Multilinear Algebra 67 (2019) 1567-1578]. Furthermore, give due to [Math. Slovaca 70 (2020), ...

Most inequality research on the relationship between inequality and mental health has focused on cross-country variation. Findings from within-country data are mixed. We examined whether changes in municipal Gini index or in the share of people living in relative poverty were linked to changes in the use of antidepressants in several Finnish municipalities between 1995 and 2010. We found that m...