Sentence examples for concept of contraction from inspiring English sources

4.01pm GMT Aubrey Meyer played a key role in developing the concept of "Contraction and Convergence" (C&C) in the early 1990s.

On the other hand, Hadzic et al. extended the concept of contraction to the multi valued case [5].

In 2012, Wardowski [17] introduced a new concept of contraction, and he proved a fixed point theorem which generalizes the Banach contraction principle.

In this literature review, we start from looking at the paper of Wardowski [14] who introduced a new concept of contraction, called F-contraction.

Before proving our fixed point theorems, we first introduce a new concept of contraction in PGM-spaces, which is a corresponding version of Sehgal's contraction in PM-spaces.

In the article, we introduce a new concept of contraction and prove a fixed point theorem which generalizes Banach contraction principle in a different way than in the known results from the literature.

Such a contraction was proved to be useful for multivalued mappings while it generalizes the previous concept of C-contraction.

Inspired and motivated by the above facts, in this paper, we introduce new concepts of contraction mappings.

First we introduce new concepts of contraction mappings, then we establish certain best proximity point theorems for such kind of mappings in metric spaces.

It is an easy matter to see that if ϕ is a comparison function or a ( c ) -comparison function, then ϕ ( t ) < t for all t > 0 and ϕ ( 0 ) = 0. Berinde [26, 27] initiated the concept of weak contraction mappings, the concept of almost contraction mappings and the concepts of ( ϕ, L ) -weak contractions.

In 1977, Alber et al. [1] generalized Banach's contraction principle by introducing the concept of weak contraction mappings in Hilbert spaces.