Definition
6
[2BH]Let
\[ F_ a =\{ xβ A : π(x) β€ a\} \quad ; \]
we always assume that \(F_ a\) is non-empty and that \(β π(x) β 0\) for each \(x β E_ a\).
We call local minimum point of \(f\) bound to \(F_ a\) a point of \(F_ a\) that is of local minimum for \(f|_{F_ a}\); and similarly for maxima.