Study On The Stability Of Functional Equations In Random Normed Spaces,Matrix Fuzzy Normed Spaces,etc

In 1940,Ulam proposed a question about the stability of group homomorphisms,the stability of functional equation we are going to study is derived from this problem.Subsequently,Hyers partially answered Ulam’s question,which led to the first result on the stability of functional equations.Later more scholars joined the study of stability of functional equations.In this paper,we study the stability of functional equations on Banach spaces,random normed spaces,modular spaces and matrix fuzzy normed spaces by applying the direct method and the fixed point approach.The main results are as follows:1.We give the solution of the multi-mixed cubic-quartic functional equation,and use the direct method to prove its stability in random normed spaces,we also use the fixed point approach to prove its stability in Banach spaces.2.We apply the fixed point approach and the direct method to prove the stability of n-dimensional quartic set-valued functional equation in Banach spaces,respectively.3.We get the solution of multi-quartic functional equation,and prove its stability in modular spaces by using the direct method.4.We obtain the solution of quintic functional equation,and use the fixed point approach to prove its stability in matrix fuzzy normed spaces.