Sentence examples for using the following theorem from inspiring English sources

We show this using the following theorem.

Therefore, the Morozov discrepancy rule of Equation (22) is modified using the following theorem.

The relationship between game and VI is usually verified using the following theorem proposed in the reference [19].

In [[7]], Shang and Zhang obtained three solutions for a perturbed Dirichlet boundary value problem involving the p-Laplacian by using the following Theorem A.

According to Hassard et al. [46] and using the quantity analysis above, the Hopf-bifurcation properties are determined using the following theorem.

By using the following theorem, the decay rate of Fourier transforms of refinable functions (phi^{m,l,alpha}_{0}) with the mask (tau^{m,l,alpha}_{0} omega)) is analyzed.

In the sequel, we will use the following theorem.

We use the following theorem to prove our main results.

Also, we will use the following theorem from [12].

The proof of Theorem 3.4 uses the following theorem, proved by I. Blank in [9].

In the next section, where we prove our main estimates, we use the following theorem.