Some Results About Stability Of Several Functional Equations

Homomorphism is an important concept of mathematics and useful in many subjects. A homomorphism can be characterized by a proper equation. An interest-ing question is that when a mapping satisfies approximately the equation, whether it is approximate to a homomorphism. The study on this question forms the so-called Hyers-Ulam-Rassias stability problem.In this article, we study the Hyers-Ulam stability of several functional equations in different conditions.In Chapter1, we describe the stability of a generalized Cauchy-Jensen func-tional equation in diffirent conditions. Firstly, we describe the characteristic of it’s explicit solution, prove that the solution is an additive mapping. Then we study it’s Hyer-Ulam stability using Rassias’method and fixed point theorem.In Chapter2, we study the Hyer-Ulam stibility of the generalized Cauchy-Jensen functional equation and I-type functional equation on C*-algebra. We prove that the solution is a*-homomorphism on a proper con-dition.