Sentence examples for using the preceding inequality from inspiring English sources

Using the preceding inequality and (3), the third equation of system (1) yields - z Δ t = c t h x t ≥ H c t x γ t ≥ c t F G α z α β t ∫ T 2 t a τ ∫ T 1 τ b s Δ s α Δ τ γ = c t F G α γ z α β γ ∫ T 2 t a τ ∫ T 1 τ b s Δ s α Δ τ γ.

The terms on the right-hand side of the preceding inequality can be estimated by using the Hölder inequality, Minkowski inequality, Poincaré inequality and Lemma 2.2.

Since E is strictly convex, the preceding inequality implies x1=x2.

Taking (ntoinfty) in the preceding inequality we immediately find the uniqueness of Q. □.

and so, by interchanging role of x, y in the preceding inequality, (3.25).

Such an extremal is unique and therefore the preceding inequality holds as an equality.

In connection with the preceding inequality (J), we notice that Tasković [10] considered a special case of this condition.

The preceding inequality holds as m n + 1 ≤ 1 ≤ ( m − n ), so that M 1 n, 1 m = | 1 n − 1 m |.

As for the first-order variation, using the preceding Lemma 4.6, (4.17).

Several key factors were identified using the PRECEDE-PROCEDE framework.

We used the precede-proceed model for the needs assessment.