Stability Of Several Kinds Of Additive Functional Equations

In this paper, we consider the Hyers-Ulam stability problems of three different functional equations deriving from additive and quadratic functions on fifferent spaces respectively. The methods we used are direct method and fixed point methods.The thesis is divided into four sections.In chapter 1, we give some fundamental knowledge of functional equations.In chapter 2, we prove the stability problem of the additive and quadratic func-tional equation in matrix Banach space, where f:Xâ†'Y is a function, X is matrix normed space and Y is matrix Banach space.In chapter 3, we prove the stability problem for additive and quadratic functional equation in Banach space, where f:Xâ†'Y is a function, X is normed space and Y is Banach space.In chapter 4, we prove the stability problem for additive and quadratic functional equation (?)n∈N,n≥2, where f:Xâ†'Y is a function, X is β-normed left B-module and Y is β-normed left Banach B-module.