On the sets of exact and approximate solutions

Abstract

We consider the problem how big is the set of solutions of a given functional equation in the set of approximate solutions. It happens that in the cases of linear functional equations (like Cauchy, Jensen) or linear inequalities (like convex, Jensen convex) the sets of solutions are very small subsets of the sets of approximate solutions. The situation is different in the cases of superstable equations (like exponential or d'Alembert).