Stability of Functional Equations

A basic question in the theory of functional equations is as follows: When is it true that a function, which approximately satisfies a functional equation, must be close to an exact solution of the equation? If the problem accepts a unique solution, we say the equation is stable. The first stability problem concerning group homomorphisms was raised by Ulam in 1940 and affirmatively solved by Hyers. In 1978 Th.M. Rassias generalized the Hyers result to approximately linear mappings. In this book, we present the general solutions of several functional equations, and we investigate the stability of these functional equations.