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].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
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