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

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 ...

extensions of some polynomial inequalities to the polar derivative

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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....

On Several Matrix Kantorovich-Type Inequalities

New Integral Inequalities Through the phi-Preinvexity

Abstract. In this note, we give some estimates of the generalized quadrature formula of Gauss-Jacobi type for phi-preinvex functions.