The Stability Of Several Types Of Functional Equations

In this paper investigate mainly give the stability of the(α，γ)additive functional equation[27]in quasi-β-Banach space and(β,ρ)-Banach space.Then we gives the stability of the new quadratic function equation on the restricted domain of quasi-β-Banach space.According to the content of this article is divided into the following four chapters:The first chapter outlines some of the basic knowledge of the major and related theoretical sources.In chapter two,let X is a linear space,Y is the quasi-β-Banach space,f:X → Y is a mapping.the method of fixed point and direct method are used to prove the(α,γ)additive functional equation f(x + y)+ αf(αz)= γ-1f(γ(x+y+z)in the quasi-β-Banach space stability problem.In chapter three,let x is the linear space,Y is the(β,ρ)-Banach space,f:X → Y is a mapping.we prove the(α,γ)additive functional equation by fixed point method and direct method.f(x + y)+ αf(αz)=γ-1f(γ(x+y+z)in the(β,ρ)-Banach space stability problem.The fourth chapter,let R is the real space,G is the commutative group,Y is the quasi-β-Banach space,and f:X → Y is a mapping,use the direct method to prove the following functions.(?)(f(x1+xj)+f(x1-xj)=2(k-1)f(x1)-2(?)f(xj)The stability problem in the restricted domain of the quasi-β-anach space.