One of the interesting questions concerning the stability problems of functional equations is as follows: when is it true that a mapping satisfying a functional equation approximately must be close to the solution of the given functional equation? Such an idea was suggested in 1940 by Ulam 1 . The case of approximately additive mappings was solved by Hyers 2 . In 1978, Rassias 3 generalized Hye...

In this paper we study the Ulam-Hyers stability of some linear and nonlinear dynamic equations and integral equations on time scales. We use both direct and operatorial methods and we propose a unified approach to Ulam-Hyers stability based on the theory of Picard operators (see [29] and[34]). Our results extend some recent results from [25],[26], [8], [14], [13] to dynamic equations and are mo...

We argue that Ulam-Hyers stability concept is quite significant in realistic problems in numerical analysis, biology and economics. A generalization to nonlinear systems is proposed and applied to the logistic equation (both differential and difference), SIS epidemic model, Cournot model in economics and a reaction diffusion equation. To the best of our knowledge this is the first time Ulam-Hye...

We study the Hyers-Ulam stability theory of a four-variate Jensen-type functional equation by considering the approximate remainder φ and obtain the corresponding error formulas. We bring to light the close relation between the β-homogeneity of the norm on F *-spaces and the approximate remainder φ, where we allow p, q, r , and s to be different in their Hyers-Ulam-Rassias stability.

The question concerning the stability of group homomorphisms was posed by Ulam 1 . Hyers 2 solved the case of approximately additive mappings on Banach spaces. Aoki 3 provided a generalization of the Hyers’ theorem for additive mappings. In 4 , Rassias generalized the result of Hyers for linear mappings by allowing the Cauchy difference to be unbounded see also 5 . The result of Rassias has bee...

In this paper, the authors established the generalized Ulam Hyers stability of additive functional equation    

In this paper, we prove the generalized Hyers-Ulam(or Hyers-Ulam-Rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.

In this work, we will prove the Hyers–Ulam stability of linear partial differential equations of first order.

in this paper, we prove the hyers-ulam stability of the symmetric functionalequation $f(ph_1(x,y))=ph_2(f(x), f(y))$ in random normed spaces. as a consequence, weobtain some random stability results in the sense of hyers-ulam-rassias.

in this paper, we prove the generalized hyers-ulam(or hyers-ulam-rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.