in this paper, we use the de nition of fuzzy normed spaces givenby bag and samanta and the behaviors of solutions of the additive functionalequation are described. the hyers-ulam stability problem of this equationis discussed and theorems concerning the hyers-ulam-rassias stability of theequation are proved on fuzzy normed linear space.

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

We will consider the Banach space valued differential equation y′(t) = Ay(t) , where A is an n× n complex matrix. We give a necessary and sufficient condition in order that the equation have the Hyers-Ulam stability. As a Corollary, we prove that the Banach space valued linear differential equation with constant coefficients y(n)(t) + an−1y(n−1)(t) + · · ·+ a1y′(t) + a0y(t) = 0 has the Hyers-Ul...

The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers’s theorem was generalized by Aoki 3 for additive mappings. In 1978, Rassias 4 generalized Hyers theorem by obtaining a unique linear mapping near an approximate additiv...

In 1940, Ulam [1] proposed the following stability problem: “When is it true that a function which satisfies some functional equation approximatelymust be close to one satisfying the equation exactly?” Next year, Hyers [2] gave an answer to this problem for additive mappings between Banach spaces. Furthermore, Aoki [3] and Rassias [4] obtained independently generalized results of Hyers’ theorem...

We obtain the general solution of the generalized quartic functional equation f(x + my) + f(x - my) = 2(7m - 9)(m - 1)f(x) + 2m²(m² - 1)f(y)-(m - 1)² f(2x) + m²{f(x + y) + f(x - y)} for a fixed positive integer m. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stab...

Abstract In this paper, a class of nonlinear ? -Hilfer fractional integrodifferential coupled systems on bounded domain is investigated. The existence and uniqueness results for the are proved based contraction mapping principle. Moreover, Ulam–Hyers–Rassias, Ulam–Hyers, semi-Ulam–Hyers–Rassias stabilities to initial value problem obtained.

In this paper, the authors investigate the generalized Ulam-Hyers stability of  n dimensional quadratic functional equation

‎In this paper‎, ‎we establish the Hyers--Ulam--Rassias stability and the Hyers--Ulam stability of impulsive Volterra integral equation by using a fixed point method‎.

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.