The stability problem of functional equations started with the question concerning stability of group homomorphisms proposed by Ulam 1 during a talk before a Mathematical Colloquium at the University of Wisconsin, Madison. In 1941, Hyers 2 gave a partial solution of Ulam’s problem for the case of approximate additive mappings in the context of Banach spaces. In 1978, Rassias 3 generalized the t...

The functional equation f(3x) = 4f(3x−3)+f(3x− 6) will be solved and its Hyers-Ulam stability will be also investigated in the class of functions f : R → X , where X is a real Banach space. Keywords—Functional equation, Lucas sequence of the first kind, Hyers-Ulam stability.

In this article, we study the Mittag-Leffler-Hyers-Ulam and Mittag-Leffler-Hyers-Ulam-Rassias stability of a class of fractional differential equation with boundary condition.

In this paper, we investigate the generalized Hyers Ulam Rassias stability of a new quadratic functional equation f(2x + y) + f(2x− y) = 2f(x + y) + 2f(x− y) + 4f(x)− 2f(y). Generalized Hyers-Ulam-Rassias Stability K. Ravi, R. Murali and M. Arunkumar vol. 9, iss. 1, art. 20, 2008 Title Page

By using a fixed point method, we establish the Hyers–Ulam stability and the Hyers–Ulam–Rassias stability for a general class of nonlinear Volterra integral equations in Banach spaces. 2000 Mathematics Subject Classification: Primary 45N05, 47J05, 47N20, 47J99, Secondary 47H99, 45D05, 47H10.

Using the fixed point method, we prove the Hyers–Ulam stability of the Cauchy–Jensen functional equation and of the Cauchy–Jensen functional inequality in fuzzy Banach ∗-algebras and in induced fuzzy C-algebras. Furthermore, using the fixed point method, we prove the Hyers–Ulam stability of fuzzy ∗-derivations in fuzzy Banach ∗-algebras and in induced fuzzy C-algebras. Published by Elsevier Ltd

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.

We obtain the Hyers-Ulam stability and modified Hyers-Ulam stability for the equations of the formg(x+p)=φ(x)g(x) in the following settings: |g(x+p)−φ(x)g(x)| ≤ δ, |g(x+p)−φ(x)g(x)| ≤φ(x), |(g(x+p)/φ(x)g(x))−1| ≤ψ(x). As a consequence we obtain the stability theorems for the gamma functional equation.

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 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.