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Best approximation in metric spaces

Author: Roshdi Khalil
Journal: Proc. Amer. Math. Soc. 103 (1988), 579-586
MSC: Primary 41A65; Secondary 54E35
MathSciNet review: 943087
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Abstract: A metric space $ \left( {X,d} \right)$ is called an $ M$-space if for every $ x$ and $ y$ in $ X$ and for every $ r \in \left[ {0,\lambda } \right]$ we have $ B\left[ {x,r} \right] \cap B\left[ {y,\lambda - r} \right] = \left\{ z \right\}$ for some $ z \in X$, where $ \lambda = d\left( {x,y} \right)$. It is the object of this paper to study $ M$-spaces in terms of proximinality properties of certain sets.

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Keywords: Midpoint, $ M$-space, convex set
Article copyright: © Copyright 1988 American Mathematical Society