In this paper, we establish the Hyers–Ulam–Rassias stability of ring homomorphisms and ring derivations on fuzzy Banach algebras.

* Correspondence: baak@hanyang. ac.kr Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea Full list of author information is available at the end of the article Abstract In this article, we prove the Hyers-Ulam stability of exact second-order linear differential equations. As a consequence, we show the Hyers-Ulam stability of the fo...

In this paper, we investigate the general solution and the generalized Hyers-Ulam stability of a new functional equation satisfied by $f(x) = x^{24}$, which is called quattuorvigintic functional equation in intuitionistic fuzzy normed spaces by using the fixed point method.These results can be regarded as an important extension of stability results corresponding to functional equations on norme...

We show that generalizations of some (classical) results on the Hyers-Ulam stability of functional equations, in several variables, can be very easily derived from a simple result on stability of a functional equation in single variable.

We prove the generalized Hyers-Ulam-Rassias stability of a partitioned functional equation. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with partitioned functional equations in Banach algebras.

We use the fixed point method to prove the probabilistic Hyers–Ulam and generalized Hyers–Ulam–Rassias stability for the nonlinear equation f (x) = Φ(x, f (η(x))) where the unknown is a mapping f from a nonempty set S to a probabilistic metric space (X ,F,TM) and Φ : S×X → X , η : S → X are two given functions. Mathematics subject classification (2000): 39B52, 39B82, 47H10, 54E70.

In this paper we are going to study the Hyers{Ulam{Rassias typesof stability for nonlinear, nonhomogeneous Volterra integral equations with delayon nite intervals.

We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.  

In this work, we present sufficient conditions in order to establish different types of Ulam stabilities for a class higher integro-differential equations. particular, consider new kind stability, the σ-semi-Hyers-Ulam which is some sense between Hyers–Ulam and Hyers–Ulam–Rassias stabilities. These result from application Banach Fixed Point Theorem, by applying specific generalization Bielecki ...

In this paper, we obtain the general solution of a generalized cubic functional equation, the Hyers-Ulam-Rassias stability, and the stability by using the alternative fixed point for a generalized cubic functional equation