Sentence examples for extend inequality from inspiring English sources

Let extend inequality (35) to Z≥2 non-negative scalars x 1,…,x Z.

Using the Hermite-Hadamard inequality for the convex function, we can extend inequality (3.1) on the left and on the right hand side as follows: (34).

We can extend inequality (1.9) given in the previous section to matrices by using the Frobenius inner product as follows: Let.

Here, (lambdacirc Koplus_{p} mucirc L) denotes the (L_{p} -Blaschke combination of K and L_{p} -Blaschkeend inequality (1.2) to general (L_{p})-mixed-brightness integrals.

To prove that formula (2.4.2) holds for arbitrary functions f in (B_{infty,1}^m({mathbb R})), we have to extend inequality (2.4.3) to the class (B_{infty,1}^m({mathbb R})).

In this paper, we first extend inequality (1.10) to dual quermassintegrals forms, that is, the extremums of dual quermassintegrals for the polars of general (L_{p} -projection bodies are obtained.

For several results which generalize, improve and extend inequalities (1.1), we refer the interested reader to [2 18].

In Section 3, we extend inequalities proved in Section 2 from the scalars setting to a Hilbert space operator setting.

Among other results, we obtain a refinement of inequality (5) and we also extend inequalities (2), (3) and (5) to the function (f(t)=t^{p}) ((pinmathcal{R})).

for t > 0, which extends inequality (14).

In [3] (see also [4]), Elbert extended inequality (2) to the one-dimensional p-Laplacian equation.