Sentence examples for using this theorem we from inspiring English sources

Using this theorem, we obtain some interesting corollaries.

Using this theorem, we prove our main result.

Using this theorem, we get a new result.

Using this theorem, we obtained the rate of pointwise convergence and gave an example including graphical illustration.

Using this theorem, we obtain three new results for finding a solution of an equilibrium problem, a fixed point of a hemirelatively nonexpnasive mapping, and a zero point of maximal monotone operators in a Banach space.

Using this theorem, we obtain three new strong convergence results for finding a solution of an equilibrium problem, a fixed point of a hemirelatively nonexpnasive mapping, and a zero point of maximal monotone operators in a Banach space.

By using this uniqueness theorem, we can omit the repeated proof for uniqueness of the relevant solutions of those equations.

Using this uniqueness theorem, we do not need to repeat the proof of uniqueness in studying the stability of functional equations mentioned above.

In this section, using the theorem, we get an upper bound for the error of our method, and we proved that the order of convergence is a (O(h^{zeta })).

if is a real positive number, then the definitions of and are equivalent, hence By using and from this theorem, we obtain We have the following two cases.

We use this theorem to establish an existence theorem for fuzzy fractional integral equations.