Nearest points and delta convex functions in Banach spaces

Jonathan M. Borwein, Ohad Giladi

Given a closed set $C$ in a Banach space $(X,\Vert \cdot \Vert )$, a point $x\in X$ is said to have a nearest point in $C$ if there exists $z\in C$ such that $d_C(x)=\Vert x-z\Vert$, where $d_C$…