Sentence examples for metric generated by from inspiring English sources

The metric generated by the norm (3) on (H_{alpha}) is called the Hölder metric.

We call this metric (d_{S}) as the metric generated by S in the case (d_{S}) is a metric.

The manifold M can be interpreted as a Riemannian manifold (M, g) where g is the metric generated by a x, D).

Moreover, if we put J = d, where d : X × X → [ 0, ∞ ) is the usual metric, then N J is a fuzzy metric generated by d.

Let (X, S) be a complete S-metric space, ((X,d_{S})) be the metric space obtained by the metric generated by S, and T be a self-mapping of X.

It follows from [1, 2] that if ω is a modular on X, then the modular space X ω can be equipped with a (nontrivial) metric generated by ω and given by d ω ( x, y ) = inf { λ > 0 : ω λ ( x, y ) ≤ λ }. for any x, y ∈ X ω.

We call the metric (S_{d}) as the S-metric generated by d.

We call the function (S_{rho }) defined in Lemma 2.3 (1) as the S-metric generated by the metric (rho.) It can be found an example of an S-metric which is not generated by any metric in [4, 9].

If the S-metric is generated by a metric d on X, then it can be easily seen that the function (d_{S}) is a metric on X, especially we have ( d_{S} x,y)=4d x,y)).

This paper presents a new method for matching metric maps generated by mobile robots that act cooperatively.

Denote by (d_{q}(cdot,cdot )) and (d_{widehat{H}}(cdot,cdot)) the distance function and Hausdorff metric, respectively, generated by (Vert cdot Vert _{q}).