If is a Banach space, then Proposition 3.7 is Proposition in [4].
Let X = [ 0, ∞ ) and define G p ( x, y, z ) = max { x, y, z } for all x, y, z ∈ X. Then ( X, G p ) is a GP-metric space. Proposition 1.1 [43].
So ( X, d ) is a complete metric space (see Proposition 2.1 of [36]).
The following consequence of Theorem 3.3 is known in our G-convex space theory: Proposition 5.3.
Then (operatorname{SAP}_{T}(X)) is a Banach space (see Proposition 3.5, [9]).
We first observe that ( R 1, ρ ) is a metric space (see Proposition 4.1 below).
To prove this, first notice that P A ( B 0 ) ⊆ A 0. Since X is a global NPC space, by Proposition 20, we obtain that P A : X → A is a continuous mapping.
In 2006, Dhompongsa et al. [4] showed that (A({ x_{n}})) consists of exactly one point for each bounded sequence ({x_{n}}) in a (operatorname{CAT}(0)) space (see Proposition 7 in [4])).
However, the proof of Theorem 4.1 does not depend on the argument techniques in [6], the inequality in 2-uniformly smooth Banach spaces (see Proposition 2.1), and the inequality in smooth and uniform convex Banach spaces (see Proposition 2.2).
(v) Cai and Bu's proof in [[3], Theorem 3.1] depends on the argument techniques in [6], the inequality in 2-uniformly smooth Banach spaces (see Proposition 2.1) and the inequality in smooth and uniform convex Banach spaces (see Proposition 2.2).
However, the proof of our Theorem 3.1 does not depend on the argument techniques in [6], the inequality in 2-uniformly smooth Banach spaces (see Lemma 1.1), and the inequality in smooth and uniform convex Banach spaces (see Proposition 1.1).
