Sentence examples for by using a contraction from inspiring English sources

By using a contraction technique, Hadar is able to show that the dynamical system has a unique equilibrium which is globally stable.

In Section 3, we prove the local existence and uniqueness of solutions for the associated regularized Novikov equation (2) by using a contraction argument.

For both cases, under suitable conditions we prove the existence and uniqueness of solutions to SRFDEs by using a contraction principle and the method of successive approximations.

Thus system (2.11) is affine (it consists of a sum of a linear transformation and a constant) and, therefore, by using a contraction argument, it admits a unique local solution defined on some time interval [ 0, T ].

In order to ensure strong convergence, in the past years, the method has been modified in several directions: by Ishikawa [4] using a double convex-combination, by Halpern [5] using an anchor, by Moudafi [6] using a contraction mapping, by Nakajo and Takahashi [7] using projections.

Recently, Ricarte and Romaguera [[8], Theorem 2.2] established the following new fuzzy version of Matowski's theorem by using a type of contraction introduced in the fuzzy intuitionistic context by Huang et al. [9], and that generalizes C-contractions as defined by Hicks in [10].

In this paper, some new generalization of Darbo's fixed point theorem is proved by using a (F psi,varphi -contraction in terms of a measure of noncompactness.

We also generalize the α-Meir-Keeler contraction by using a more general expression in the contractive condition.