Grüss Inequality And Various Forms Of Kantorovich Inequality

The purpose of this paper is to discuss the Frobenius inner product versions of Grüss type inequalities,we also prove the Kronecker product forms of Kantorovich type inequalities after establish Grüss type inequalities,and the last a direct proof for a Kantorovich type inequality in the complex domain due to the theory optimization is presented.This paper is divided into three sections according to contents.Chapter 1 This part, we discuss the Frobenius inner product versions of the generalizations of Grüss inequality and itself. Meanwhile, with the numerical radius, we show the matrix formulation of matrix trace and its numerical radius.Chapter 2 We define Linearly ordered and Similarly ordered, later proof the Kronecker product forms of chebyshev inequality, Grüss type inequalities and Kantorovich type inequalities.Chapter 3 In this section, the proof of a Kantorovich type inequality in the complex domain by Bauer and Householder is creative.