Sentence examples for corollary is valid from inspiring English sources

By the direct method, the following corollary is valid in the (Archimedean) Banach spaces.

So, for any linearization technique, using the clipping as a PAPR reduction, Corollary 2 is valid.

If A is a totally nonnegative matrix, Corollary 3.4 is valid, so we obtain the result in [11].

Since generalized Meir-Keeler α-contractions are Meir-Keeler α-contractions, then Corollary 9 is valid also for Meir-Keeler α-contractions.

(ii) Corollary 3.15 is valid for partially ordered fuzzy metric spaces in the sense of Kramosil and Michálek, so it is also valid for fuzzy metric spaces in the sense of George and Veeramani.  .

Corollary 3.15 is valid for partially ordered fuzzy metric spaces in the sense of Kramosil and Michálek, so it is also valid for fuzzy metric spaces in the sense of George and Veeramani.

Corollary 3.1 The function f t, u) = σ(t)u, where σ (t) ≤ L is admissible in Theorem 3.1 to yield u(t) ≤ 0 on t0 ≤ t ≤ T. Observe that a dual result of corollary 2.1 is valid.

To convince ourselves that Corollary 1.3 is valid, it suffices to note that if conditions (1.22 - 1.24) are fulfilled, then each of conditions (1.11), (1.16), (1.17) is satisfied iff α < 2 + μ and β > 2 + μ.

The following example shows that the previous corollary is not valid in non-Archimedean spaces.

The following example shows that the previous corollary is not valid in non-Archi-medean Banach spaces.

Hence, we prove that (ii) is valid by Corollary 1.