There's loads more. How about for How about Don't forget linear combinations of functions such as these, although I'm not sure that linear combinations of downward-sloping convex functions are necessarily downward-sloping and convex. Still, I imagine you could find a number of examples.
I don't think you're going to be able to come up with a general formula for all downward-sloping convex functions. The issue here is that the most information you have is that
That is not enough information to determine
[EDIT] Absolutely LOVE your signature. That is a pet peeve of mine as well, which is one reason I detest research papers. One book you might find interesting is N. David Mermin's book Boojums All the Way Through.