Sentence examples for mean inequality in from inspiring English sources

We link some equivalent forms of the arithmetic-geometric mean inequality in probability and mathematical statistics.

Using the weighted arithmetic-geometric mean inequality in (2), we get (26).

Let us start with a simplified case of the mean inequality in equation (4.6).

The arithmetic-geometric mean inequality (in short, AG inequality) has been widely used in mathematics and in its applications.

Using the weighted arithmetic-geometric mean inequality in (2), ∏ 2 ( G 1 ⊗ G 2 ) is less than or equal to (22).

(iii) We leave to the reader the routine task for obtaining more mean inequalities in a similar way to previously.

He applied this function to prove the integral means inequality in [19], that is for all f ∈ T, η > 0 and 0 < r < 1 ∫ 0 2 π | f ( r e i θ ) | η d θ ≤ ∫ 0 2 π | f 2 ( r e i θ ) | η d θ.

If (q,q_{1},q_{2}in(-1,0)) then the mean-inequalities in the previous proposition are reversed.

In summary, the stability and stabilizability concepts are good tool for obtaining a lot of mean-inequalities in a short and nice manner.

Exploring the stabilizability concept, recently introduced by Raïssouli, we give an approach for obtaining refinements of mean-inequalities in a general point of view.

As already pointed before, this section displays some important applications of the above concepts for refining mean-inequalities in a general point of view.