The Studies Of The Ulam Stability Of Fuzzy Number-valued Functional Equations

In this paper,we main study the Ulam stability problem of fuzzy number-valued functional equations in Banach spaces.The main work includes the following two parts.In the first part,we focus on studying the Ulam stability problem of fuzzy functional equations in Banach spaces.Firstly,by considering bounded function differences and with the metric defined on a fuzzy number space,the Ulam stability of four kinds of fuzzy functional equations can be proved in Banach spaces.We obtain that there must be a unique exact solution near the approximate solution of a given equation under some appropriate conditions.Secondly,we generalize quadratic type and Drygas type fuzzy functional equations in more general forms.Moreover,considering unbounded function differences,which together with the properties of metric,we discuss their Ulam stability in Banach spaces.We can still get a unique exact solution near the approximate solution of a given equation under some appropriate conditionsIn the second part,we main investigate the Ulam stability of fuzzy differential equations in Banach spaces.With the metric and different differentiabilities,we prove the Ulam stability of three kinds of fuzzy differential equations in two different cases.It is proved that under appropriate conditions,there must be a exact differential solution near the approximate solution of a given equation.