Sentence examples for homogeneous means from inspiring English sources

Let (m_{1}), (m_{2}) be two homogeneous means.

The next result, giving us a lot of power homogeneous means, is of great interest.

For this end, we need the following lemma, which tells us an inequality for bivariate homogeneous means can be equivalently changed into the form of hyperbolic functions.

Corollary 3.2 Let m 1 and m 2 be two homogeneous means such that m 1 π r = m 2 π r for a certain r ∈ ] 0, 1 [.

We introduce some symmetric homogeneous means, and then we show unitarily invariant norm inequalities for them, applying the method established by Hiai and Kosaki.

We here define a few symmetric homogeneous means using P α ( x, y ) and Q α ( x, y ) in the following way.

(M_{f,k}) is a homogeneous mean.

Let m be a homogeneous mean.

Let (kin{mathcal {K}}) and m be a homogeneous mean.

(6.1) is a homogeneous mean, symmetric provided (lambda=1/2).

A four-parameter homogeneous mean is defined by another approach.