Sentence examples for dual inequality from inspiring English sources

In the same paper, the so-called dual inequality (1.11).

Finally, we get the following dual inequality of the inequality (1.22).

Namely, we complete the proof of Theorem 1.2 and Theorem 1.3 (i.e., dual inequality of Theorem 1.2) in the introduction.

We can prove a dual inequality of (2.3) in a similar way as in Proposition 2.1 stated as follows.

In particular, Γ − p B = B. Si Lin gives the following dual inequality of inequality (1.8) (see [[13], p.9, Theorem 5.4]).

Besides, applying these concepts, we establish the extension results of the well-known L p -Petty affine projection inequality, L p -Busemann centroid inequality and its dual inequality.

Based on this phenomenon and with the verification by computer, we can propose some dual inequalities for the results presented in this paper.

By the dual Minkowski inequality we can obtain the dual Brunn-Minkowski inequality (see [10]): For (M,Ninmathcal{S}_{o}^{n}) and (lambda, mugeq0), we have V lambda M,tilde,mu N ^{frac{1}{n}}leqlambda V(M ^{frac{1}{n}}+mu V(N ^{frac{1}{n}} (2.6) with equality if and only if M and N are dilates.

or the equivalent dual variational inequality (see Lemma 2.2) (3.13).

It is also the dual of inequality (3.2). (Positive multisublinear).

which is equivalent to its dual variational inequality (3.31).