2009 / March Volume 4 No.1
On metric spaces in which metric segments have unique prolongations
| Published Date |
2009 / March
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|---|---|
| Title | On metric spaces in which metric segments have unique prolongations |
| Author | |
| Keyword | |
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| Pagination | 1-8 |
| Abstract | An M-space is a metric space $(X, d)$ having the property that for each pair of points $p, q \in X$ with $d(p, q) = \lambda$ and for
each real number $\alpha \in [0, \lambda]$, there is a unique $r_\alpha \in X$ such that
$d(p, r_\alpha) = \alpha$ and $d(r_\alpha, q) = \lambda - \alpha$. In an M-space $(X, d)$, we say that metric segments have unique prolongations if points $p, q, r, s$ satisfy $d(p, q) + d(q, r) = d(p, r), d(p, q) + d(q, s) = d(p, s)$ and $d(q, r) = d(q, s)$ then $r = s$.
This paper mainly deals with some results on best approximation in metric spaces for which metric segments have unique prolongations. |
| AMS Subject Classification |
41A65, 52A05, 51M30
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| Received |
2008-02-05
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| Accepted |
2008-02-05
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