Sentence examples for using the previous theorem from inspiring English sources

By using the previous theorem we have.

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

Next, using the previous two theorems, we obtain the needed two-sided Hardy-type inequalities.

Using the previous proposition, we have the following theorem.

In this section we use the previous theory to obtain a fixed point theorem for multifunctions in the Banach space.

Using the previous result, we get the following generalizations of Sherman's theorem for 2n-convex functions.

Using the previous example, search for television.

Without appealing to potentials, but by using different means, the result of the previous theorem also holds for systems.

The previous theorem also holds using a weaker contractivity condition.

Now, we discuss the weighted version of the Grüss inequality which is used to generalize the previous Theorems 3.2 and 3.3.

Remark 13 In the previous theorem, we have only used the continuity of ∗ at ( 1, 1 ), that is, if { x n }, { y n } ⊂ [ 0, 1 ] are sequences such that { x n } → 1 and { y n } → 1, then { x n ∗ y n } → 1.