Sentence examples for implies the inequality for from inspiring English sources

Since (sqrt{frac{3}{pi}}<1), the asymptotic result implies the inequality for large values of s.

We will show that the condition implies the inequality for all, where and are constants defined in Definition 2.11 and the triangle inequality for, respectively.

The positivity of the operator implies that the inequality follows from the inequality It is clear that the inequality for implies the inequality for Now according to Lemma 2.9, we obtain that for.

We prove also that the weak initial inequality on E0 and the strong functional differential inequality (5) imply the inequality for (t, x) ∈ E, 0 < t ≤ a. Lemma 2.3.

for all ; (3) for each, which implies the inequality (4.37)  . for each, which implies the inequality (4.37).

for all ; (3) for every, which implies the inequality (4.15)  . for every, which implies the inequality (4.15).

It is clear now that the inequality for positivity of and nonnegativity of for imply the inequalities   for  .

for all., which implies the inequality.

for all ; (3), which implies the inequality  ., which implies the inequality.

for all ; (3), which implies the inequality (3.25).

For the first case (sin[0,tau]), by the fact that (V s,t,omega bar {x}_{0}) is continuous with respect to ((s,bar{x}_{0})) and uniformly continuous with respect to s for (sin[0,tau]), there exists (delta=delta epsilon)>0) such that (|x_{0}-hat{x}_{0}| leqdelta) implies the inequality (|V s,0,omega bar{x}_{0}|