SOME INEQUALITIES FOR BIVARIATE MEANS

Companion Inequalities for Certain Bivariate Means

Sharp companion inequalities for certain bivariate means are obtained. In particular, companion inequalities for those discovered by Stolarsky and Sándor are established.

An Optimal Inequalities Chain for Bivariate Means

Abstract. Let p ∈ R , M be a bivariate mean, and Mp be defined by Mp(a,b) = M1/p(ap,bp) (p = 0) and M0(a,b) = limp→0 Mp(a,b) . In this paper, we prove that the sharp inequalities L2(a,b) < P(a,b) < NS1/2(a,b) < He(a,b) < A2/3(a,b) < I(a,b) < Z1/3(a,b) < Y1/2(a,b) hold for all a,b > 0 with a = b , where L(a,b) = (a− b)/(loga − logb) , P(a,b) = (a− b)/[2arcsin((a−b)/(a+b))] , NS(a,b) = (a−b)/[2ar...

Some means inequalities for positive operators in Hilbert spaces

In this paper, we obtain two refinements of the ordering relations among Heinz means with different parameters via the Taylor series of some hyperbolic functions and by the way, we derive new generalizations of Heinz operator inequalities. Moreover, we establish a matrix version of Heinz inequality for the Hilbert-Schmidt norm. Finally, we introduce a weighted multivariate geometric mean and sh...

Some Comparison Inequalities for Generalized Muirhead and Identric Means

Some Inequalities for Operator Means and Hadamard Product

We prove some general theorems which unify results on arithmetic-geometric mean and some other related matrix inequalities. As an application we obtain some results involving Hadamard product of matrices. Mathematics subject classification (2010): 47A30 15A60.