On Several Matrix Kantorovich-Type Inequalities

On Several Matrix Kantorovich-Type Inequalities

Several Matrix Euclidean Norm Inequalities Involving Kantorovich Inequality

where λ1 ≥ · · · ≥ λn > 0 are the eigenvalues of A. It is a very useful tool to study the inefficiency of the ordinary least-squares estimate with one regressor in the linear model. Watson 1 introduced the ratio of the variance of the best linear unbiased estimator to the variance of the ordinary least-squares estimator. Such a lower bound of this ratio was provided by Kantorovich inequality 1....

Kantorovich type inequalities for ordered linear spaces

In this paper Kantorovich type inequalities are derived for linear spaces endowed with bilinear operations ◦1 and ◦2. Sufficient conditions are found for vector-valued maps Φ and Ψ and vectors x and y under which the inequality Φ(x) ◦2 Φ(y) ≤ C + c 2 √ Cc Ψ(x ◦1 y) is satisfied. Complementary inequalities are also given. Some results of Dragomir [J. Inequal. Pure Appl. Math., 5 (3), Art. 76, 20...

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.

Ela Kantorovich Type Inequalities for Ordered Linear Spaces∗

In this paper Kantorovich type inequalities are derived for linear spaces endowed with bilinear operations ◦1 and ◦2. Sufficient conditions are found for vector-valued maps Φ and Ψ and vectors x and y under which the inequality Φ(x) ◦2 Φ(y) ≤ C + c 2 √ Cc Ψ(x ◦1 y) is satisfied. Complementary inequalities are also given. Some results of Dragomir [J. Inequal. Pure Appl. Math., 5 (3), Art. 76, 20...