Sentence examples for order contraction from inspiring English sources

Since is an order contraction mapping, is order continuous.

From order contraction of it follows that is order continuous.

Since is an order contraction mapping, for a.e., we have (3.8).

If is an order contraction mapping, then there exists a unique random fixed point in.

The main result of this subsection is as follows, which extends the conclusion of the Banach fixed point theorem (Theorem 1.2) to higher-order contraction mappings: (Higher-order contraction mapping theorem).

Both (first-order) contraction mappings and the rth-order contraction mappings defined in Theorem 1.3 are special cases of the now-proven generalised Banach contraction conjecture (see Jachymski [8], Merryfield-Stein [9] and Arvanitakis [10]).

In Section 3, we demonstrate that the conclusions of Theorems 1.2 and 1.3 extend to all higher-order contraction mappings.

The main result of this paper is to extend the Banach fixed point theorem (and an often-cited generalisation) to higher-order contraction mappings.

Let ((mathcal{X},d) ) be a complete metric space and let (T:mathcal{X}tomathcal{X} ) be an rth-order contraction mapping.

We begin with a direct proof of the fixed point theorem for higher-order contraction mappings; thereafter, we provide a re-metrisation argument that relates higher-order Lipschitz mappings to (first-order) Lipschitz mappings.

T is an rth-order contraction mapping if the polynomial (p z):=z^{r}-sum_{k=0}^{r-1}c_{k}z^{k}) is stable, that is, (|lambda|<1) if (p lambda)=0 ).