Study On The Stability Of Functional Equations In Some Spaces

The problem of the stability of functional equations originated from a question on the stability of group homomorphism proposed by Ulam.D.H.Hyers partially answered Ulam's question,thereby obtaining the first result on the stability of functional equations.Subsequently,this result aroused the research interests of many scholars.In this paper,by using the direct method and the fixed point approach,we investigate the stability of functional equations in quasi fuzzy(?,p)-normed spaces,random normed spaces,matrix?-normed spaces and(n,?)-normed spaces.The main contents include:1.we use the fixed point approach to consider the stability of a mixed type quartic,cubic and quadratic functional equation in quasi fuzzy(?,p)-normed spaces.2.we first give the general solution of generalized quartic functional equation,and then discuss its stability in matrix ?-normed spaces by the direct method and the fixed point approach,respectively.3.we adopt the direct method to study the stability of ?-type mixed additive quadratic functional equation in random normed spaces.4.we introduce the solution of generalized septic functional equation,and investigate its stability in random normed spaces by the direct method.