Is difference between a convex function and a affine function convex?
See http://mathworld.wolfram.com/AffineFunction.html for definition of affine function.
All affine functions are conevx and concave. Not all convex or concave functions are afffine.
One dimensional examples:
f(x) = 2 + 3*x is a comvex affine function (conxex and affine). It is also concave affine.
f(x) = x^2 is a convex function, but is not affine.