Study On The Stability Of Functional Equations In(n,β)-Normed,Matrix Random Normed Spaces,Etc.

In 1940,the mathematician Ulam first presented the famous Ulam stability problem.In the next year,Hyers proved that stability of additive equation in Banach spaces by using the direct method.Aoki and Rassias extended the result of Hyers by turning the control constant in Hyers method into an unbounded function.Subsequently,the stability of problems for the functional equations have been extensively studied.In this paper,we investigate the stability of functional equations in random(n,β)–normed spaces,intuitionistic fuzzy n–normed spaces,matrix random normed spaces,(n,β)–normed spaces and fuzzy –normed spaces.The main results are as follows:1.We define random(n,β)–normed spaces and give the general solution of the r–variable quadratic functional equation,βthen prove the stability of r–variable quadratic functional equation in random(n,β)–normed spaces by using the direct method and fixed point method,respectively.2.We give the solution of the generalized octic functional equation,βand use the direct and fixed point methods to prove the stability of the generalized octic functional equation in intuitionistic fuzzy n–normed spaces.3.We get the general solution of the m–dimensional additive functional equation,βand prove the stability of the m–dimensional additive functional equation in matrix random normed spaces by using the direct and fixed point methods.4.We adopt the direct method to prove the stability of the η–type mixed additive and quartic functional equation in(n,β)–normed spaces,and the direct and fixed point methods to prove its stability in fuzzy –normed spaces.