The Stability Of Several Types Of Functional Equations

In this paper investigate mainly give the stability of the(???)additive functional equation[27]in quasi-?-Banach space and(?,?)-Banach space.Then we gives the stability of the new quadratic function equation on the restricted domain of quasi-?-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-?-Banach space,f:X ? Y is a mapping.the method of fixed point and direct method are used to prove the(?,?)additive functional equation f(x + y)+ ?f(?z)= ?-1f(?(x+y+z)in the quasi-?-Banach space stability problem.In chapter three,let x is the linear space,Y is the(?,?)-Banach space,f:X ? Y is a mapping.we prove the(?,?)additive functional equation by fixed point method and direct method.f(x + y)+ ?f(?z)=?-1f(?(x+y+z)in the(?,?)-Banach space stability problem.The fourth chapter,let R is the real space,G is the commutative group,Y is the quasi-?-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-?-anach space.