Suppose V is a vector spaceMathworldPlanetmath (over a field), and f is a function f:V. Then f is subadditive if



  1. 1.

    Any linear functionMathworldPlanetmath V is subadditive.

  2. 2.

    If is a norm on V, a0, then


    is subadditive.


Suppose f is subadditive.

  1. 1.

    If f is positively 1-homogeneousPlanetmathPlanetmathPlanetmathPlanetmath, then f is convex.

  2. 2.

    The sum of two subadditive functions is subadditive.

Title subadditive
Canonical name Subadditive
Date of creation 2013-03-22 15:12:26
Last modified on 2013-03-22 15:12:26
Owner matte (1858)
Last modified by matte (1858)
Numerical id 7
Author matte (1858)
Entry type Definition
Classification msc 46B20
Related topic LinearTransformation
Related topic Seminorm
Related topic HomogeneousFunction