Study On The Stability Of Functional Equations In Matrix ?–normed Spaces And Fuzzy ?–normed Spaces,etc

The stability of functional equations originated from the stability of group homomorphisms proposed by Ulam.Hyers answers Ulam's questions in the Banach space section.In this paper,we study the stability of functional equations in matrix ?–normed spaces,fuzzy ?–normed spaces,quasi(?,p)–normed spaces,fuzzy(n,?)–normed spaces and matrix random normed spaces.The main results are as follows:1.Use the direct method to prove the stability of Cauchy–Jensen–Pexider functional equation in matrix –normed spaces,fuzzy ?–normed spaces.2.Give the general solution of m–dimensional quintic functional equation.The direct method is used to prove the stability of m–dimensional quintic functional equation in quasi(?,p)–normed spaces.The fixed point approach and the direct method are used to prove the stability of fuzzy ?–normed spaces.3.Define fuzzy(n,?)–normed spaces and give solution of m–dimensional additive functional equation.The stability of m–dimensional additive functional equation in fuzzy(n,?)–normed spaces is proved by the direct method and the fixed point approach,respectively.4.Give the general solution of m–dimensional sextic functional equation.The direct method and the fixed point approach are used to prove the stability of m–dimensional sextic functional equation in the matrix random normed spaces and fuzzy ?–normed spaces,respectively.