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

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

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.

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

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.

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.

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

In this section, we first recall the concentration compactness principle in the setting of the fractional p-Laplacian and then investigate the mountain-pass geometry and the behavior of the ((PS)) sequence.

In this section, we present some extensions of Banach contraction principle in the setting of partial cone metric spaces over a non-normal solid cone of an abstract normed vector space.

Generalizing the concept of metric space, Bakhtin [15] introduced the concept of b-metric space which is not necessarily Hausdorff and proved the Banach contraction principle in the setting of a b-metric space.

Although Branciari [3] correctly stated the analog of Banach contraction mapping principle in the setting of Branciari metric space, proofs has gaps which was removed by a number of authors; see e.g. [5, 12, 19, 31].