Sentence examples for retraction onto from inspiring English sources

We define the radial retraction onto (mathrm{B}_{n}) as follows: r(x):=frac{x}{max{1,mu(x)}}, quad mbox{for } xin X, where μ is the Minkowski functional on (mathrm{B}_{n}), i.e., (mu(x)=inf{alpha>0:xinalphamathrm{B}_{n}}).

sunny if for each x ∈ C and t ∈ [ 0, 1 ], we have Π C [ t x + ( 1 − t ) Π C ] = Π C x ; a retraction of C onto K if Π C x = x, ∀ x ∈ K ; a sunny nonexpansive retraction if Π C is sunny, nonexpansive and retraction onto K.

In this paper, we prove some theorems to guarantee the existence of nonexpansive retractions onto the common fixed points of some families of (weakly) asymptotically nonexpansive (type) mappings.

We prove some theorems for the existence of ergodic retractions onto the set of common fixed points of a family of asymptotically nonexpansive mappings.

[7]If E is a uniformly smooth Banach space, C1and closedconvex convex subsets of E such that the Hausdorff distance H ( C 1, C 2 ) ≤ δ, and Q C 1 and Q C 2 are the sunny nonexpansive retractions onto the subsets C1and C2, respectively, then ∥ Q C 1 x - Q C 2 x ∥ 2 ≤ 1 6 R ( 2 r + d ) h E 1 6 L δ R, (2.17).

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

A subset of is called a sunny nonexpansive retract of if there exists a sunny nonexpansive retraction from onto.

Definition 4.6. is said t be a sunny nonexpansive retract of if there exists a sunny nonexpansive retraction of onto.

A subset of is said to be a sunny nonexpansive retract of if there exists a sunny nonexpansive retraction of onto.

A subset of is called a nonexpansive retract of if either or there exists a retraction of onto which is a nonexpansive mapping.

Let be the sunny nonexpansive retraction of onto.