Sentence examples for by the previous theorem from inspiring English sources

By the previous theorem, we have the following immediate corollary.

Then, by the previous theorem, provides for each.

The unique set given by the previous theorem is called the attractor of the GIFS.

By the previous theorem, if f and g are not compatible, then f cannot be G-continuous at ω.

Thus by the previous theorem we see that the origin of the system (3) is exponentially stable.

By (1.1), f satisfies (4.1) and by the previous theorem (m^{sigma_{k}}) is a homogeneous mean.

By using the previous theorem we have.

Then by applying the previous theorem Razumikhin class R c is a convex cone (also closed).

Since k-NUC implies NUC and NUC implies property (H), by using the previous theorem, we can give the following result.

Now by applying the previous theorem, we get G ( E ) = Λ 0 q ( t α − s / n w 1 ) ∩ Λ 0 r ( t β − s / n w 2 ), and the couple ( E, G ( E ) ) is optimal.

Now, we present an example to illustrate the obtained result given by the previous theorems.