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as weakly convergence in.
So admits a weakly convergence subsequence.
By '⇀' we denote the weakly convergence.
In [21] a weakly convergence theorem for -asymptotically quasi-nonexpansive mapping defined in Hilbert space was proved.
Because lim n → ∞ ∥ x n − x ∗ ∥ exists, which implies { x n } is bounded, hence { x n } has a weakly convergence subsequence { x n j }.
Since lim n → ∞ ∥ x n − x ∗ ∥ exists, { x n } is bounded and hence { x n } has a weakly convergence subsequence { x n j }.
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Our convergence analyses guarantee that the algorithm weakly converges to a solution under certain assumptions.
Since is an arbitrary weakly convergent sequence of, we can conclude that convergence strongly to.
We write x n ⇀ x to indicate that the sequence { x n } weakly converges to x and x n → x will symbolize strong convergence as usual.
We write x n ⇀ x to indicate that the sequence { x n } weakly converges to x; as usual, x n → x will symbolize strong convergence.
Then the sequence ({x_{n}}) weakly converges to a common element of Ω. Next, we establish the strong convergence theorems of our iteration.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com