# Strongly quasiconvex function

($LaTeX: f$ on $LaTeX: X$). $LaTeX: X$ is a convex set and $LaTeX: \textstyle f(a \, {x} + (1-a)\, y) < \max\{f(x), f(y)\} \mbox{ for all } {x}, y \in X,$ with $LaTeX: \textstyle x \ne y,$ and $LaTeX: \textstyle a \in (0, 1).$