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Convex Bodies and Hypersurfaces

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Abstract

The concept of a convex set can be introduced in any linear space L. A set K in L is called convex if the line segment ab is contained in K for any elements a, b ∈ K, i.e. \({x_{t}} = \left( {1 - t} \right)a + tb \in K \) for any a, b ∈ K and any t ∈ [0,1].

Keywords

  • Convex Hull
  • Convex Body
  • Convex Cone
  • Convex Combination
  • Supporting Function

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1994 Springer-Verlag Berlin Heidelberg

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Bakelman, I.J. (1994). Convex Bodies and Hypersurfaces. In: Convex Analysis and Nonlinear Geometric Elliptic Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69881-1_1

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  • DOI: https://doi.org/10.1007/978-3-642-69881-1_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-69883-5

  • Online ISBN: 978-3-642-69881-1

  • eBook Packages: Springer Book Archive