Is the product of strictly quasiconcave functions quasiconcave?
Solution 1:
The answer is no. A simple example will suffice. Consider the L 1/2 norm and a shifted L 1/2 norm.
Now, if two non-negative quasi-convex functions have the same optimal point, then the product is quasi-convex. I think there are some other cases where this works.
Another question might be: is it possible to combine two quasi-convex functions into a new quasi-convex function. And the answer is, yes it is! Suppose that $f_1$ and $f_2$ are quasi-convex. Then $f=\max(f_1,f_2)$ is a quasi-convex function.