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Journal of Convex Analysis 14 (2007), No. 3, 455--463
Copyright Heldermann Verlag 2007

Direction of Movement of the Element of Minimal Norm in a Moving Convex Set

Renu Choudhary
Dept. of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand


We show that if $K$ is a nonempty closed convex subset of a real Hilbert space $H$, $e$ is a non-zero arbitrary vector in $H$ and for each $t\in \mathbb{R}$, $z(t)$ is the closest point in $K + te$ to the origin, then the angle $z(t)$ makes with $e$ is a decreasing function of $t$ while $z(t)\neq 0$, and the inner product of $z(t)$ with $e$ is increasing.

Keywords: Moving convex set, nearest point projection.

MSC: 46C05; 47H99, 41A65

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