Let $C$ be a nonempty closed convex subset of a real Hilbert space $X$, and let $x \in X$. Then there exists a unique point $P_{C}x \in C$ such that $\left\Vert x - P_{C}x \right\Vert = \min_{y \in C} \left\Vert x-y \right\Vert$. Moreover, this point is characterized by $$ P_{C}x \in C \quad \text{and} \quad \left( \forall y \in C \right) ~ \left< x-P_{C}x ~ , ~ y-P_{C}x \right> \leq 0. $$ I happened to know that this characterization is (or was) known as the Bourbaki-Cheney-Goldstein inequality and started to look around for book references but could not find one. (This characterization is known to me as "obtuse angle criterion" or "projection theorem.")
My question is: Is there any book that refers to the above characterization as "Bourbaki-Cheney-Goldstein"? I am curious about this and it would be nice to know the reason behind this name.
Any help would be highly appreciated.
Refer to that book written by P.G.Ciarlet, Linear and Nonlinear Functional Analysis with Applications, Theorem 4.3-1.