Sentence examples for using conclusion from inspiring English sources

Arguing as in the proof of Theorem 3.1, but using conclusion (c) of Theorem 2.4 instead of (b), one establishes the following result.

Replacing the condition at infinity of the potential F by a similar one at zero, and arguing as in the proof of Theorem 3.1 but using conclusion (b) of Theorem 2.1 instead of (a), one establishes the following result.

We observe in Theorem 3.1 we can replace ξ → +∞ and (t1,..., t n ) → with ξ → 0+ (t1,..., t n ) → (0+,..., 0+), respectively, that by the same way as in the proof of Theorem 3.1 but using conclusion (c) of Theorem 2.1 instead of (b), the system (1) has a sequence of weak solutions, which strongly converges to 0 in X.

By using Conclusions 4.1 and 4.2, ({T_{n}}) is a uniformly closed family of countable quasi-Bregman ((2n+1))-pseudocontractive mappings.

By using Conclusions 4.1 and 4.2, ({T_{n}}) is a uniformly closed family of countable Bregman quasi-Lipschitz mappings with the condition (lim_{nrightarrowinfty}L_{n}=lim_{nrightarrowinfty}frac{n+1}{n}=lim_{nrightarrowinfty}frac{n+1}{n

end{cases} Since (4.2) holds, by using Conclusions 4.1 and 4.2, we know that ({ T_{n}}) is a uniformly closed family of countable quasi-Bregman ((2n+1))-pseudocontractive mappings.

Most texts used conclusions that were not derived from the evidence used.

As many different treatments were used conclusions cannot be made regarding an optimal treatment schedule.

Using the conclusion of Theorem 2.1, we finish the proof of Theorem 2.2.

Again, using the conclusion (iii) of Lemma 2.3, we have, where.

By using the conclusion of contraction mapping principle in Banach space, we complete our proof.