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Since is uniformly smooth and strictly convex, by Remark 2.1 ii) it yields that is hemi-continuous.
When, it yields that.
Indeed, it yields that (24).
For any, it yields that.
It yields that σ = 0.
Note that is hemicontinuous, it yields that.
In view of Lemma 2.5, it yields that (3.7).
It yields that, which proves the uniqness of.
and hence for any, it yields that (3.7).
In view of (3.12), it yields that and.
Note that J-1: E* → E is hemicontinuous, it yields that y λ, n ⇀ x*.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com