Sentence examples for map is single from inspiring English sources

Since the duality map is single valued and weakly continuous, we obtain, by (3.1), that (317).

Since the duality map is single valued and weakly sequentially continuous from to, we get that (3.48).

Using that the duality map is single valued and weakly sequentially continuous from to, by (2.15), we get that.

Following Browder [22], we say that a Banach space has a weakly continuous duality map if there exists a gauge for which the duality map is single valued and weak-to-weak* sequentially continuous (i.e., if is a sequence in weakly convergent to a point, then the sequence converges weakly* to ).

It is said to be uniformly Frechet differentiable (and is said to be uniformly smooth) if the limit in (2.1) is attained uniformly for It is well known that a Banach space is uniformly smooth if and only if the duality map is single valued and norm-to-norm uniformly continuous on bounded sets of.

Since the duality map is single-valued and weakly continuous, we get that (3.52).

It is known that a Banach space is Fréchet differentiable if and only if the duality map is single-valued and norm-to-norm continuous.

A Banach space is uniformly smooth if and only if the duality map is single-valued and norm-to-norm uniformly continuous on bounded sets of.

It is well know that if is smooth, then the duality mapping is single valued.

A Banach space is said to be smooth if the duality mapping is single valued.

The duality mapping is said to be weakly sequentially continuous if the duality mapping is single valued and for any with,.