Sentence examples for mappings are continuous from inspiring English sources

It is easy to verify that these mappings are continuous (although the mapping (pmapsto f_{p}) is not continuous for (p=0)), so they are exponentially convex.

Since these mappings are continuous (although the mapping s ↦ g s is not continuous for s = 0 ), so s ↦ Φ i ( x, y ; p, g, g s ) ( i = 1, 2 ) are exponentially convex.

Since these mappings are continuous (although the mapping s ↦ g s is not continuous for s = 0 ), s ↦ Φ i ( x, y ; g s ) ( i = 1, 2 ) are exponentially convex.

It is easy to see that these mappings are continuous, so they are exponentially convex.

In the entire text, all topological spaces are metric and all single-valued mappings are continuous.

Primitives of HK and HL integrable mappings are continuous (see [[6], Theorem 7.4.1]).

There are some classical results available concerning the case when one of the self-mappings is continuous or when both self-mappings commute [25].

Notice that the mappings (F_{y}) are continuous and affine.

Regarding that the mappings and are continuous, is closed for each.

The given condition (3.38) of strict continuity implies that a fixed point of is unique (if it exists) and that both mappings and are continuous.

Since are uniformly -Lipschitzian mappings, so and are continuous mappings.