Sentence examples for using this equality and from inspiring English sources

Using this equality and Proposition 14, one can state the following result.

So, the result follows by using this equality and Proposition 10. □.

Using this equality and (16), we get | M | ≤ C w | λ | for  λ ∈ G w. Thus, lim N → ∞ I N = 0.

Using this equality and replacing C1and C2 by their expressions from equations (14) and (15) lead to the following equation: x C dec. N CSymb = ( y − 1 ) C dem + ( M ).

Using this equality in (4.5), we have (4.8).

Using this second equality and equalizing terms by terms, we obtain the following lemma.

Then, by using the equality and the above estimates, we get (4.14).

The effectiveness of challenge questions using the equality and relaxed algorithms is discussed below.

Table 3 shows the crosstab analysis of data using the equality and relaxed algorithms under columns 3 to 6 headings.

Generalizing this, using these equalities and considering fractional Steffensen's inequality for conformable fractional integrals, we get a new version of weighted Iyengar-type integral inequalities for conformable integrals.

We now use the equality and have (3.17).