Sentence examples for by using the ideas from inspiring English sources

Theorem 2.3 can be proven by using the ideas in the proof of [30], Theorem 2.

By using the ideas of the proofs of Theorems 2.5 and 2.3, we easily prove the following theorem.

Theorem 2.2 can be proven by using the ideas presented in the proof of [28], Theorem 3.3.

The directions to search for fixed points are generated by using the ideas of the steepest descent direction and conventional nonlinear conjugate gradient directions for unconstrained optimization.

Next, we provide the accelerated Picard algorithm by using the ideas of conjugate gradient methods that accelerate the steepest descent method.

One could also obtain a multivalued version of Theorem 2.18 by using the ideas in the proof below with the ideas in [16].

Cartan had investigated how much may be accomplished in differential geometry by using the idea of moving frames of reference.

In this section, we establish the asymptotically optimal AOR method by using the idea of [5 7].

In [17], Korovkin type approximation theorems were proved by using the idea of statistical convergence.

Here we extend the capability of the method to rare probability computation by using the idea of importance sampling (IS).

Proof By using the idea of [[22], p.47], we can get the conclusions of Lemma 2.6 easily.