Sentence examples for principle in the setting of from inspiring English sources

One of the main results from [31] is the Banach contraction principle in the setting of normal cone spaces.

We present a new generalization of the Banach contraction principle in the setting of Branciari metric spaces.

One of the most useful generalizations of the Banach contraction principle in the setting of metric spaces is known as Caristi's fixed point theorem.

In particular, Geraghty [6] obtained a generalization of the Banach contraction principle in the setting of complete metric spaces by considering an auxiliary function.

Matthews [1] introduced the notion of a partial metric space and extended Banach contraction principle in the setting of partial metric space.

Using the Hausdorff metric, Nadler Jr. [1] has established a multivalued version of the well-known Banach contraction principle in the setting of metric spaces as follows.

In 2008, Al-Homidan et al. [1] established Ekeland-type variational principles in the setting of quasi-metric spaces with a Q-function.

Remark 2.4 Theorem 2.1 extends the famous Banach contraction principle to that in the setting of cone b-metric spaces.

While representing a US perspective, underlying principles apply globally in the setting of magistral and extemporaneous formulations produced outside national regulatory frameworks.

They gave the version of the Banach contraction principle and other basic theorems in the setting of cone metric spaces.

The well-known Banach contraction principle and its several generalizations in the setting of metric spaces play a central role for solving many problems of nonlinear analysis.