Sentence examples for by using the idea from inspiring English sources

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

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

By using the idea of multivalued contraction mappings in [11, 12], Alfuraidan introduced the following concept of a G-contraction.

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

By using the idea of Green's functions, every solution ((f,g,h)) to BVP (2.1) can be expressed by left.

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

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.

One could obtain a multivalued version of Theorem 2.37 by using the ideas in the proof below with the ideas in [16].