A counterexample to the infinity version of the Hyers and Ulam stability theorem.

Hyers and Ulam proved a stability result for convex functions, defined
in a subset of W . Here we give an example showing that their result
cannot be extended to those functions defined in infinite-dimensional normed
spaces. Also, we give a positive result for a particular class of approximately
convex functions, defined in a Banach space, whose norm satisfies the so-called
convex approximation property.