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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 survey the problem of studying the size of the set of points in $X$ which have nearest points in $C$ . We then turn to the topic of delta convex functions and indicate how it is related to finding nearest points.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
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