Definition:Maximum Value of Real Function/Local/Strict

Definition

Let $f$ be a real function defined on an open interval $\openint a b$.

Let $\xi \in \openint a b$.

$f$ has a strict local maximum at $\xi$ if and only if:

$\exists \openint c d \subseteq \openint a b: \forall x \in \openint c d: \map f x < \map f \xi$

A strict local maximum is also known as a strict relative maximum.

Some sources refer to this as a local maximum and do not consider the situation where $\forall x \in \openint c d: \map f x \le \map f \xi$.

Some sources assume local as given, and merely refer to this as a maximum or strict maximum.