Sentence examples for extension of contraction from inspiring English sources

We show that by using this extension of contraction theory to nondifferentiable vector fields, it is possible to design observers for a large class of piecewise smooth systems using not only Euclidean norms, as also done in previous literature, but also non-Euclidean norms.

From Theorem 2.4, by taking (k_{4}=0), we obtain the extension of Reich contraction.

One of the most interesting is the study of the extension of Banach contraction principle to the case of non-self-mappings.

Remark 3.1 Note that the Corollary 3.3 is a proper extension of the contraction mapping principle [13] because the continuity of the mapping T is not required.

Recently, Ma et al. [11] presented their work on the extension of Banach contraction principle for (C^ -algebra-valued metriC^ -algebra-valued

The results presented in the paper are an extension of the Banach contraction principle, the Suzuki contraction theorem, and the Jleli and Samet fixed point theorem.

It is undeniable that Rhoades's weak contraction is one of the earliest and the most important extensions of the contraction principle.

In this paper, we present an extension of the Edelstein contraction theorem for cyclic contractions in a fuzzy metric space.

In the present paper, an extension of the Edelstein contraction theorem for cyclic contractions in a fuzzy metric space is established, which also can be considered as a generalization of the fuzzy Edelstein contraction theorem introduced by Grabiec.

Geraghty [16] introduced an extension of the Banach contraction principle in which the contraction constant was replaced by a function having some specified properties.

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.