Sentence examples for be a retraction from from inspiring English sources

Let c be a retraction from E onto F(S) obtained by Lemma 3.6.

Let be a closed convex subset of a smooth Banach space, let be a nonempty subset of, and let be a retraction from onto.

Let be a convex subset of a smooth Banach space, be a nonempty subset of and be a retraction from onto.

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

Let C be a nonempty closed and a sunny generalized nonexpansive retraction of a smooth, strictly convex Banach space E, and let R be a retraction from E to C. Then the following are equivalent: (1) R is sunny generalized nonexpansive;   (2) (langle x-Rx, Jy-JRxrangleleq0) for all (xin E) and (yin C).  .

Let C be a nonempty closed convex subset of a smooth Banach space and Q C be a retraction from E onto C. Then the following are equivalent: (i) Q C is both sunny and nonexpansive;   (ii) 〈 x − Q C x, J ( y − Q C x ) 〉 ≤ 0 for all x ∈ E and y ∈ C.  .

Furthermore, is a sunny nonexpansive retraction from onto if is a retraction from onto which is also sunny and nonexpansive.

A function such that for all is a retraction from to in.

Furthermore, Q is a sunny nonexpansive retraction from C onto D if Q is a retraction from C onto D which is also sunny and nonexpansive.

Q is called a sunny nonexpansive retraction from C onto D if Q is a retraction from C onto D and Q is sunny and nonexpansive.

Let D be a nonempty subset of C. A mapping Q: C → D is said to be sunny if Q ( Q x + t ( x - Q x ) ) = Q x, whenever Qx + t(x - Qx) ∈ C for x ∈ C and t ≥ 0. A mapping Q: C → D is said to be retraction if Qx = x for all x ∈ D. Furthermore, Q is a sunny nonexpansive retraction from C onto D if Q is a retraction from C onto D which is also sunny and nonexpansive.