Quasiconvex function

Level sets are convex. Equivalently, $LaTeX: X$ is a convex set and $LaTeX: \textstyle f(ax + (1-a)y) \le \max \left \{f(x), f(y) \right \} \mbox{ for all } x, y \in X$ and $LaTeX: a$ in the interval $LaTeX: [0,1].$