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arXiv · 1510.04471

Nearest points and delta convex functions in Banach spaces

Jonathan M. Borwein·Ohad Giladi
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Abstract

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

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Jonathan M. Borwein, Ohad Giladi. 2015-10-15. Nearest points and delta convex functions in Banach spaces. https://doi.org/10.1017/s000497271500101x

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