Sentence examples for mappings with sequence from inspiring English sources

Let be a nonempty bounded closed convex subset of a Hilbert space and let be a family of nonexpansive mappings with sequence.

Since is an infinite family of closed quasi- -nonexpansive mappings, it is an infinite family of closed and uniformly quasi- -asymptotically nonexpansive mappings with sequence.

Therefore, { f n } is a sequence of nearly contraction mappings with sequence { ( k n, a n ) }. Let C be a nonempty closed convex subset of a Hilbert space H.

Since { S i } i = 1 ∞ : C → C is an infinite family of closed quasi-ϕ-nonexpansive mappings, it is an infinite family of closed and uniformly quasi-ϕ-asymptotically nonexpansive mappings with sequence k n = 1.

Lemma 3 Let C be a nonempty convex subset of a hyperbolic space X, and let S, T : C → C be asymptotically nonexpansive mappings with sequence { k n } ⊂ [ 1, ∞ ) such that ∑ n = 1 ∞ ( k n − 1 ) < ∞.

Since T i i = 1 ∞ is a countable family of closed quasi-ϕ-nonexpansive multi-valued mappings, by Remark 1.5(3), it is a countable of closed and uniformly quasi-ϕ asymptotically nonexpansive multi-valued mappings with sequence {k n = 1}.

Let be uniformly -Lipschitzian nonself asymptotically quasi-non-expansive mappings with sequences such that, for all.

Let be nonself asymptotically nonexpansive mappings with sequences such that, for all satisfying condition (B).

Let be nonself asymptotically nonexpansive mappings with sequences such that for all.

Let be nonself asymptotically quasi-non-expansive mappings with sequences such that, for all.

Let be a real Banach space, a closed convex nonempty subset of, and asymptotically quasi-nonexpansive mappings with sequences (resp).