Sentence examples for methods of corollary from inspiring English sources

However, the assumptions and proof methods in Theorems 3.1 and 3.3 in [2] are different from the assumptions and proof methods of Corollary 2.2.  .

By employing the method of Corollary 3.1 in this paper, r's for different values of τ with (mu=0) are listed in Table 4.

By using the same method as that of Corollary 4.15 in Goldman et al. [1] on the interval ([0,1]), we can prove this corollary.

By using the same methods as in the proof of Corollary 3.4, the following result is obtained.

By using the same methods as in the proof of Corollary 2.1, we have the following result.

Proof Applying the same method as in the proof of Corollary 3.3 and in the proof of Lemma 2.1, we can obtain Corollary 3.5.

Taking into account the method of proof of Corollaries 6 and 7, we find that optimality (13) contains as a particular case the optimality conditions (14), (24), (25).

Proof of Corollary 1.1.

There is a stronger version of Corollary 23.

(38) The next corollary is the equivalent of Corollary 1.

The proof of Corollary 2 is similar to Corollary 1. □.