Research On The Superstability Of Several Types Of Functional Equations

In this paper,we consider the Hyperstability problems of several different functional equations on different spaces respectively.The method we used is fixed point method.The thesis is divided into three sections.In chapter 1,we give some fundamental knowledge of functional equations.In chapter 2,we prove the Hyperstability problems of the Cauchy functional equation f(x + y)= f(x)+ f(y),the Jensen functional equation 2f(x+y/2)=f(x)+f(y),quadratic functional equation f(x + y)+ f(x-y)= 2f(x)+ 2f(y),Drygas functional equation f(x + y)+ f(x-y)= 2f(x)+ f(-y)+ f(y),radical quadratic functional equation f((?))=f(x)+f(y),and radical cubic functional equation f((?))= f(x)+ f(y)in Banach space,where X is normed space and Y is Banach space and f:X ? Y is a function.We also consider the P-Wright affine functional equation f(px +(1-p)y)+ f((1-p)x + py))= f(x)+ f(y)in quasi-?-Banach space,where X is normed space,Y is quasi-?-Banach space and f:X ? Y is a function.In chapter 3,we study the Hyperstability problems of the functional equation raised above in quasi-Banach space.