Let $f : \mathbb{R}^n \to \mathbb{R}_+$ satisfy $$f(a) - f(b) \le C f(a - b)$$ $\forall a, b \in \mathbb{R}^n$ for some $C \ge 0$. Is there a name for such functions? (I would be happy to have a name for the special case $C=1$.)

Note the similarity to $$\|x\| - \|y\| \le \|x - y\|$$ which is satisfied by all norms.

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