Sentence examples for use a contraction from inspiring English sources

In this paper we use a contraction mapping method to show that if all terms in the TRT equations except possibly the opacity are discretized implicitly, then for any Δt>0, the time-discretized TRT equations (i) have a unique solution, which (ii) satisfies the maximum principle and (iii) preserves the equilibrium (thick) diffusion limit.

One classical way to find the fixed point of a nonexpansive mapping is to use a contraction to approximate it.

One classical way to study nonexpansive mappings is to use a contraction to approximate a nonexpansive mapping.

A well-known way to find a fixed point of a nonexpansive mapping is to use a contraction to approximate it (Browder [25, 26]).

In academic writing, such as all papers in college, you should never use a contraction unless it is part of a quotation.

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

Now, let us give some of the important theorems and definitions in order to solve linear and nonlinear differential equations using a contraction mapping.

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 this paper, we consider the setting of b-metric spaces to establish results regarding the common fixed points of two mappings, using a contraction condition defined by means of a comparison function.