Sentence examples for mean inequality with from inspiring English sources

This is a harmonic-geometric mean inequality with negative weights.

This is a geometric-arithmetic mean inequality with negative weights.

Next, we show the reverse arithmetic-geometric mean inequality with the Specht ratio for two positive operators.

The right side of (18) follows by a simple application of the arithmetic-geometric mean inequality with (17), and this completes the proof.

Firstly, we provide an application of the obtained results to improve Hao Z-C inequality, which is related to the generalized arithmetic-geometric mean inequality with weights.

However, using the arithmetic geometric mean inequality (with equality when y 1  = y 2  = y n, i.e. fully correlated user channels), a guaranteed lower bound on I(n) can be obtained as [18] I n ≥ ∫ 0 ∞ ⋯ ∫ 0 ∞ 1 ln 2 ln n !

Along the paper, inequality will mean inequality (I.1) with additional assumption (I.2).

Baricz and Sándor [18] pointed out that inequalities (1) and (3) are simple consequences of the arithmetic-geometric mean inequality together with the well-known Lazarević-type inequality [[19], p. 238] ( cos x ) 1 / 3 < sin x x for all 0 < x < π 2, (4).

Thus, using the arithmetic-geometric mean inequality, (L'leq0) with equality if (S=S^), (V=V^), and (I=I^).

(2.7) Combining (2.7) with the arithmetic mean-geometric mean inequality yields (2.6).

This, with (11.1), immediately yields the desired mean inequality.