Exact(36)
It follows that Since is uniformly convex and smooth, we have from Lemma 2.1 that (3.12).
On the other hand, we have that Since is strictly increasing, it follows that Hence and so.
Take, such that, and assume that Since is monotone nondecreasing, then, for all, and one also gets that (2.11).
For we have Assume that Since is the projection of onto, by Lemma 2.3, we have (3.5).
Notice from Lemma 3.4 ii) that Since is compact-valued, for each there exists and such that and It follows from (4.16) that (4.17).
By the boundedness of, we obtain that Since is continuous and the sequences and are bounded, there exists an accumulation point of such that.
Similar(24)
That has since been lifted.
That has since been reversed.
This is a notion that has since been debunked.
(This claim that has since been proved false).
That has since been disproved by scientific studies.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com