PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 39(53), pp. 149--151 (1986)
A CHARACTERIZATION OF STRICTLY CONVEX METRIC
T. D. NarangDepartment of Mathematics, Guru Nanak Dev University, Amritsar 143005, India
Abstract: A subset $G$ of a metric linear space $(E,d)$ is said to be semi-Chebyshev if each element of $E$ has at most approximation in $G$ and the space $(E,d)$ is said to be strictly convex if $d(x,0)\leq r$, $d(y,0) \leq r$ imply $d((x+y)/2,0)< r$ unless $x=y$; $y\in E$ and $r$ is any positive real number. We prove that a metric linear space $(E,d)$ is strictly convex if and only if all convex subsets of $E$ are semi-Chebyshev.
Classification (MSC2000): 41A52
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