Operator versions of the Kantorovich 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.

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

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...

Generalization on Kantorovich Inequality

In this paper, we provide a new form of upper bound for the converse of Jensen’s inequality. Thereby, known estimations of the difference and ratio in Jensen’s inequality are essentially improved. As an application, we also obtain an improvement of Kantorovich inequality.

Hadamard Product Versions of the Chebyshev and Kantorovich Inequalities

The purpose of this note is to prove Hadamard product versions of the Chebyshev and the Kantorovich inequalities for positive real numbers. We also prove a generalization of Fiedler’s inequality.