Definition:Superadditive Function (Conventional)
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Definition
Let $\struct {S, +_S}$ and $\struct {T, +_T, \preccurlyeq}$ be semigroups such that $\struct {T, +_T, \preccurlyeq}$ is ordered.
Let $f: S \to T$ be a mapping from $S$ to $T$ which satisfies the relation:
- $\forall a, b \in S: \map f a +_T \map f b \preccurlyeq \map f {a +_S b}$
Then $f$ is defined as being superadditive.
The usual context in which this is encountered is where $S$ and $T$ are both the set of real numbers $\R$ (or a subset of them).
Also see
- Results about superadditive functions can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): additive function
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): additive function