Sentence examples for is properly contained from inspiring English sources

Assume that is properly contained in.

The class of hyperbolic spaces is properly contained in the class of convex metric spaces.

Next, assume that D ¯ is properly contained inside the (deterministic) basin of attraction of u ∗.

Obviously, the classical BMO space is properly contained in BMO θ ; for more examples please see [9].

These imply that the class of τ-distance is properly contained in the class of u-distance.

Clearly v is properly contained in v ′; in fact, it is repeated three times after a particular pattern.

The following example shows that the class of demicontractive mapping is properly contained in the class of hemicontractive mappings.

Observe that T is not quasi-nonexpansive so that the class of multivalued quasi-nonexpansive mappings is properly contained in the class of multivalued demicontractive-type mappings.

The full space of all Toeplitz operators is transitive, but if B is properly contained in this space and contains allanalyticToeplitz operators, then B must be reflexive.

The following examples show that the class of nonexpansive-type mappings is properly contained in the class of k-strictly pseudocontractive-type mappings and the class of k-strictly pseudocontractive-type mappings is properly contained in the class of pseudocontractive-type mappings.

Examples to show that the class of nonexpansive-type mappings is properly contained in the class of k-strictly pseudocontractive-type mappings and that the class of k-strictly pseudocontractive-type mappings is properly contained in the class of pseudocontractive-type mappings were given in [2].