Sentence examples for be demiclosed at zero from inspiring English sources

Let S : C → C be a continuous quasi-nonexpansive mapping which is assumed to be demiclosed at zero.

The mapping (T:Hto H ) is said to be demiclosed at zero if for any sequence ({u_{n}}subset H ) with (u_{n}rightharpoonup u ) and (Tu_{n}to0), we have (Tu=0).

Let S : C → C be a continuous quasi-nonexpansive mapping which is assumed to be demiclosed at zero and let B : C → H be a β-inverse-strongly monotone mapping.

Then I − T is saide to be demiclosed at zero, if, for any ( x n ) in H, the following implication holds: x n ⇀ x ( I − T ) x n → 0 ] ⇒ x ∈ Fix ( T ).

Then I − T is said to be demiclosed at zero, if for any sequence { x n } ⊂ C with x n ⇀ x and ∥ x n − T x n ∥ → 0, x = T x.

Then the mapping T is said to be demiclosed at zero if, for any sequence { x n } n ∈ N in C which converges weakly to z, and if ∥ T x n − x n ∥ → 0 as n → ∞, then T z = z.

Then is demiclosed at zero.

Then I − S is demiclosed at zero.

Then, I - T is demiclosed at zero.

Since each is demiclosed at zero,.

Then, the mapping is demiclosed at zero.