Nearest points and delta convex functions in Banach spaces

Abstract

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 $d_C$ is the distance of $x$ from $C$. We shortly survey the problem of studying how large is the set of points in $X$ which have nearest points in $C$. We then discuss the topic of delta-convex functions and how it is related to finding nearest points.

To appear in Bull. Aust. Math. Soc

References in corpus (1)

• Sigma-porosity is separably determined