Let the Euclidean distance between two points x,y, be denoted by d(x,y):=||x-y||_2.
Given a scalar a>0, can you find a real function f s.t.


a) f>=0, and f(z) = 0 if and only if z = a.
b) f(d(x,y)) is jointly convex in (x,y).


Thanks for your help