A Study On The Stability Of Functional Equation

In this paper,we will study the stability of AQ-functional equation in quasi-(2;p)-Banach space and the stability of K-dimensional quadratic functional equations.In the first chapter,we introduce the research results of the proposed inequality,and also introduces the concept of quasi-(2;p)-Banach space and obtains the relevant properties.In the second chapter,we introduce the stability of AQ-functional equations in quasi-(2;p)-Banach space.In this chapter,we divide the mapping f into approximate even,even,approximate odd and odd.The different stability results of AQ-functional equation are obtained.In the third chapter,the stability of the K-dimensional quadratic functional equation is introduced.We will study the stability of this equation by introducing the functional index)(?kA.We obtain that if f is a mapping from a group to Banach space and bounded,then it has Hyers-Ulam-Rassias stability.This conclusion generalizes the theorems of Jae-Hyeong Bae and Kil-Woung Jun.The second part,we will study the stability of the k-dimensional quadratic functional equation over the restricted domains.