MMN-2917
Best approximation and characterization of Hilbert spaces
Setareh Rajabi;Abstract
It is well known that for any nonempty closed convex subset $C$ of a Hilbert space, any best approximation $y\in C$ of the point $x$ satisfies the inequality $\Vert x -y\Vert^{2}+\Vert z-y\Vert^{2} \leq \Vert x -z\Vert^{2}$ for all $z\in C$.
In this paper, we first introduce and study a new subset of best approximations involving this inequality in general metric spaces. Then, we provide some equivalent conditions which characterize Hilbert spaces.
Vol. 20 (2019), No. 2, pp. 1167-1173