Miscellaneous

Abstract

One of the simplest functional equations is the associativity equation. This functional equation represents the famous associativity axiom $x.(y.z)=(x.y).z$. Section 14.1 deals with the superstability of the associativity equation. In Section 14.2, an important functional equation defining multiplicative derivations in algebras will be introduced, and the Hyers–Ulam stability of the equation for functions on (0, 1] will be proved. The gamma function Г is very useful to develop other functions which have physical applications. In Section 14.3, the Hyers–Ulam–Rassias stability of the gamma functional equation and a generalized beta functional equation will be proved. The Hyers–Ulam stability of the Fibonacci functional equation will be proved in the last section.