Sentence examples for mapping is single from inspiring English sources

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

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

We know that if is smooth, strictly convex, and reflexive, then the duality mapping is single valued, one to one, and onto.

It is well know that if is smooth, strictly convex and reflexive, then the duality mapping is single valued, one-to-one and onto.

Note that the duality mapping is single valued ( is smooth), and norm topology to weak* uniformly continuous on bounded sets of Banach space with uniformly Gateaux differentiable norm.

We know that if is smooth, strictly convex, and reflexive, then the duality mapping is single valued, one to one, and onto; see [6] for more details.

The generalized duality mapping is single-valued if is strictly convex [14], or is uniformly smooth space.

It is known that a Banach space is smooth if and only if the normalized duality mapping is single-valued.

(iii) If is a smooth, strictly convex, and reflexive Banach space, then the normalized duality mapping is single-valued, one-to-one, and onto.

It is well known that if is uniformly G teaux differentiable norm, then the duality mapping is single-valued and uniformly continuous on each bounded subset of.

On the other hand, noticing that the sequence is bounded and the duality mapping is single-valued and norm to weak* uniformly continuous on bounded subsets of, we conclude that (4.11).