Sentence examples for extend the contraction from inspiring English sources

Some of the obtained results extend the contraction principle to the use of altering-distance functions and extended altering-distance functions, the last ones being piecewise continuous.

These changes in the fictive motor pattern are likely to extend the contraction phase of the muscle during one swim cycle.

The following best proximity point theorem, due to Basha [19], which extends the contraction principle to the case of non-self mappings, is a special case of Theorem 3.1.

It is clear that pointwise contractive behavior was introduced to extend the contractive behavior in Banach contraction principle [9].

Now, we extend the Banach contraction and the Kannan contraction to the so-called generalized contractive mapping as follows.

In 1976, Jungck [2] extend the Banach contraction principle to a common fixed point theorem for commuting maps.

In this section, we extend the Banach contraction principle to the class of generalized metric spaces with a partial order.

These are control functions which have been used to extend the Sehgal contraction in probabilistic metric spaces.

In this paper we extend the Banach contraction for multivalued mappings in a cone b-metric space without the assumption of normality on cones and generalize some attractive results in literature.

In 1962, Rakotch [29] extended the Banach contraction principle with replacing the contraction constant c in (1.1) by a contraction function γ and established the result later.

Cyclic maps were introduced by Kirk, Srinavasan and Veeramani [1] in 2003 to extend the celebrated Banach contraction principle [2]: In a complete metric space ( X, d ), every contraction T : X → X has a unique fixed point.