Sentence examples for and has a weakly from inspiring English sources
Lemma 1.3 Let E be a reflexive Banach space and has a weakly continuous duality map J φ ( x ) with gauge φ.
Then there holds the identity lim sup n → ∞ Φ ( ∥ x n − y ∥ ) = lim sup n → ∞ Φ ( ∥ x n − x ∥ ) + Φ ( ∥ y − x ∥ ), ∀ y ∈ E. Xu [4] showed that, if E is a reflexive Banach space and has a weakly continuous duality map J φ with gauge φ, then there is a sunny nonexpansive retraction from C onto F ( T ).
The guanine nucleotide exchange factor (GEF) domain of sec2p protein is a 22-nm long coiled coil and has a weakly interacting N-terminal region and a strongly intertwined middle region as evident from the crystal structure.
Let E be a reflexive Banach space and have a weakly continuous duality map J φ ( x ) with gauge φ.
Theorem X Let E be a reflexive Banach space and have a weakly continuous duality map J φ with a gauge φ.
Let E be a reflexive Banach space and have a weakly continuous duality map J ϕ with a gauge function ϕ.
Let X be a reflexive Banach space and have a weakly continuous duality map J φ with gauge φ, let C be a nonempty closed convex subset of X, let T : C → C be a nonexpansive mapping with Fix ( T ) ≠ ∅, and let f ∈ Ξ C. Then { x t } defined by x t = t f ( x t ) + ( 1 − t ) T x t, ∀ t ∈ ( 0, 1 ), converges strongly to a point in Fix ( T ) as t → 0 +.
Let E be a reflexive Banach space and have a weakly continuous duality map J φ with gauge φ, let C be a nonempty closed convex subset of E, let T : C → C be a nonexpansive mapping with F ( T ) ≠ ∅, and let f ∈ Π C. Then { x t } defined by x t = t f ( x t ) + ( 1 − t ) T x t, ∀ t ∈ ( 0, 1 ), converges strongly to a point in F ( T ) as t → 0 +.
The stem tissue is made of longitudinally running, cylindrical hyphae that are 5 12 µm wide, smooth, colorless, and have a weakly dextrinoid in Melzer's reagent.
If they never had a highly positive troponin level, and had a weakly positive troponin level at any time, they were categorized as weakly positive.
(3.11) Since ({x_{n}}) is a bounded sequence and it has a weakly convergent subsequence say, (x_{n_{i}}rightharpoonup x^), [10] or with the help of Opial's condition [12], we can see that (x_{n}rightharpoonup x^).
