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NEAREST POINTS AND DELTA CONVEX FUNCTIONS IN BANACH SPACES
Published online by Cambridge University Press: 03 September 2015
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 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.
MSC classification
- Type
- Research Article
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- Copyright
- © 2015 Australian Mathematical Publishing Association Inc.
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