Sentence examples for obtain this theorem from inspiring English sources

By Lemma 3.1, we can obtain this theorem.

In order to obtain this theorem, we will apply Theorem A to the functional (Phi z)).

Similarly to the proof of Theorem 4.1, we can obtain this Theorem.

In order to obtain this theorem, we apply Theorem A to the functional Φ ( z ).

We obtain this result in Theorem 2 by using Rakotch's theorem, and this will provide us with an extra information about how to obtain (sqrt{f}) as a uniform limit of functions of (mathcal{A}).

Remark 19 If in Theorem 15-Theorem 18 μ = 0, then we obtain Theorem 2.1-Theorem 2.3 of [10].

The results obtained by this theorem prove to be very useful in reducing the computational efforts when a new algorithm based on tabu search for the SRFLP is proposed in this paper.

Recently, many endpoint results have been obtained for this theorem, and in this paper we extend them to generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces.

We will compare with the result from[21], Proposition 1, where ω = 2 q p - 1, q > q ≥ 1 and the quasi-norm constant is 2 1 p. Since ( ( ω + 1 ) / 2 ) 1 q < 2 1 p we see that quasi-norm constant C obtained in this theorem is strictly less than the known constant for that case.

Then we obtain the theorem.

Therefore, we obtain the theorem below.