Sentence examples for be a retraction of from inspiring English sources

Let and be convex subsets of the Banach space, with under proper inclusion, and let be a retraction of onto.

Let D be a nonempty subset of C. Let Π be a retraction of C onto D and let J be a normalized duality mapping on X.

(see [9]) Let C be a nonempty closed subset of a smooth, strictly convex and reflexive Banach space E, and let R be a retraction of E onto C. Then the following statements are equivalent: (1) R is sunny generalized nonexpansive;   (2) 〈x - R x, J y) - J(Rx)〉 ≤ 0 for all (x, y) ∈ E × C.  .

If A ⊂ B are subsets of a topological space and π : B → A is a continuous mapping from ℬ onto A such that π ( p ) = p for every p ∈ A, then π is said to be a retraction of ℬ onto A. When a retraction of ℬ onto A exists, A is called a retract of ℬ.

Let D be a subset of B where B is a subset of a Banach space E and let P be a retraction of B onto D. Then P is said to be sunny [15] if for each x ∈ B and t ≥ 0 with P x + t ( x − P x ) ∈ B, P ( P x + t ( x − P x ) ) = P x.

Let D be a subset of B, where B is a subset of a Banach space E, and let P be a retraction of B onto D, that is, P x = x for each x ∈ D. Then P is said to be sunny if for each x ∈ B and t ≥ 0 with P x + t ( x − P x ) ∈ B, P ( P x + t ( x − P x ) ) = P x.

It is a retraction of ellipsoid drop of a polymer within the other polymer bulk.

The most common eye symptom is a retraction of the eyelids that makes the eyes appear to bulge or stare dramatically.

The second, about 30 minutes later, was a retraction of that concession, and Mr. Gore's aides have said that Mr. Bush's tone of voice led the vice president to tell him he did not have to be "snippy".

Thus, is a retraction of to.

Thus for every and is a retraction of onto.