Quasiconvex function

A function with f(λx+(1−λ)y)≤max{f(x),f(y)}

Quasiconvex function

Let $X$ be a vector space and let $f:X\to\mathbb{R}$ be extended-real-valued. The function $f$ is quasiconvex if for all $x,y\in X$ and all $\lambda\in(0,1)$ ,

f(\lambda x+(1-\lambda)y)\le \max\{f(x),f(y)\}.

Context. Quasiconvexity is weaker than convexity: every convex function is quasiconvex, but not conversely. It is important in economic modeling and level-set methods.

Examples:

Any convex function is quasiconvex.
The function $f(x)=\sqrt{|x|}$ on $\mathbb{R}$ is quasiconvex but not convex.
Any constant function is quasiconvex.