Strict local minimum ($f(x)>f(x_{\ast })(0<\Vert x-x_{\ast }\Vert <\delta )$)

A local minimum is strict when every other point of the domain of a function in some neighbourhood has a larger value. Strictness is local: two separated strict local minima can have the same value, as $x^4-2x^2$ at $\pm 1$ demonstrates. Negating the function gives a strict local maximum.