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Proceedings of the American Mathematical Society

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Metric inequalities and convexity


Author: Dorothy Wolfe
Journal: Proc. Amer. Math. Soc. 40 (1973), 559-562
MSC: Primary 52A05
DOI: https://doi.org/10.1090/S0002-9939-1973-0319045-9
MathSciNet review: 0319045
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Abstract: Conditions that a given point of a normed linear space is (or is not) a convex combination of $ n$ fixed points are given in terms of the metric. The point is said to be metrically dependent if the conditions hold.


References [Enhancements On Off] (What's this?)

  • [1] R. G. Bilyeu, Metric definition of the linear structure, Proc. Amer. Math. Soc. 25 (1970), 205-206. MR 41 #4200. MR 0259562 (41:4200)
  • [2] Marshall Hall, Jr., Combinatorial theory, Blaisdell, Waltham, Mass., 1967. MR 37 #80. MR 0224481 (37:80)
  • [3] Frederick A. Valentine, Convex sets, McGraw-Hill Series in Higher Math., McGraw-Hill, New York, 1964. MR 30 #503. MR 0170264 (30:503)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0319045-9
Keywords: Normed linear space, metric space, convex combinations, extreme points
Article copyright: © Copyright 1973 American Mathematical Society

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