Sentence examples for version of contraction from inspiring English sources

By the same token, the uptick in December garnered lots of attention because it carried Chinese manufacturing across the dividing line between contraction and expansion.In this section Crazy aunt on the loose The case for the defence Horns of a dilemma China's version of contraction Rich managers, poor clients Half-cocked Basel Called to account Downturn, start up ReprintsOr did it?

In [7], author stated that the F-contraction is the modified version of Banach contraction principle.

In 1969, Nadler [1] established the multivalued version of Banach contraction principle.

Obviously, Theorem 1.2 is an extensive version of Banach contraction principle.

By using Definition 2.4, Sankar Raj in [10] gave an extended version of the contraction mapping principle in [21].

Grabiec [4] presented a fuzzy version of Banach contraction principle in a fuzzy metric space of Kramosi and Michalek's sense.

Thus, we can apply for F the b-metric space version of the contraction principle given by Czerwik (see, for example, Theorem 12.2, p.115 in [40]) and we get the conclusion.

In this paper, we have proposed an extended version of the Edelstein contraction theorem for cyclic contraction mappings in a fuzzy metric space, which can be considered as a generalization of the fuzzy Edelstein contraction theorem introduced by Grabiec [1].

Beiranvand, Moradi, Omid, and Pazandeh [7] introduced the notion of a T-contraction and established a version of the Banach contraction principle.

Instead, we use a modified version of the Laplacian contraction, and these boundary points contract normally along the inward curvature flow in normal directions as inner points.

Nadler [12] has proved a multi-valued version of the Banach contraction principle which states that each closed and bounded value contraction map on a complete metric space has a fixed point.