subadditive
Suppose $V$ is a vector space^{} (over a field), and $f$ is a function $f:V\to \mathbb{R}$. Then $f$ is subadditive if
$$f(x+y)\le f(x)+f(y),x,y\in V.$$ 
Examples

1.
Any linear function^{} $V\to \mathbb{R}$ is subadditive.

2.
If $\parallel \cdot \parallel $ is a norm on $V$, $a\ge 0$, then
$$f(x)=a+\parallel x\parallel $$ is subadditive.
Properties
Suppose $f$ is subadditive.

1.
If $f$ is positively $1$homogeneous^{}, then $f$ is convex.

2.
The sum of two subadditive functions is subadditive.
Title  subadditive 

Canonical name  Subadditive 
Date of creation  20130322 15:12:26 
Last modified on  20130322 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 