Improved Young and Heinz inequalities with the Kantorovich constant

Improved Variants of Young, Heinz, and Hölder Inequalities for Matrices

In this talk we deal with a more precise estimates for the matrix versions of Young, Heinz, and Hölder inequalities. First we give an improvement of the matrix Heinz inequality for the case of the Hilbert-Schmidt norm. Then, we refine matrix Young-type inequalities for the case of Hilbert-Schmidt norm, which hold under certain assumptions on positive semidefinite matrices appearing therein. Fin...

Improvements of Young inequality using the Kantorovich constant

‎Some improvements of Young inequality and its reverse for positive‎ ‎numbers with Kantorovich constant $K(t‎, ‎2)=frac{(1+t)^2}{4t}$‎ ‎are given‎. ‎Using these inequalities some operator inequalities and‎ ‎Hilbert-Schmidt norm versions for matrices are proved‎. ‎In‎ ‎particular‎, ‎it is shown that if $a‎, ‎b$ are positive numbers and‎ ‎$0 leqslant nu leqslant 1,$ then for all integers $ kgeqsl...

New progress on the operator inequalities involving improved Young’s and its reverse inequalities relating to the Kantorovich constant

The purpose of this paper is to give a survey of the progress, advantages and limitations of various operator inequalities involving improved Young's and its reverse inequalities related to the Kittaneh-Manasrah inequality. We also present our new progress to the related research topics. New scalar versions of Young's inequalities are promoted, the operator version and the Hilbert-Schmidt form ...

Foliations and Chern-Heinz inequalities

We extend the Chern-Heinz inequalities about mean curvature and scalar curvature of graphs of C2-functions to leaves of transversally oriented codimension one C2-foliations of Riemannian manifolds. That extends partially Salavessa’s work on mean curvature of graphs and generalize results of Barbosa-Kenmotsu-Oshikiri [3] and Barbosa-GomesSilveira [2] about foliations of 3-dimensional Riemannian ...

On Several Matrix Kantorovich-Type Inequalities