Introduction A classical question in the theory of functional equations is “when is it true that a mapping, which approximately satisfies a functional equation, must be somehow close to an exact solution of the equation?”. Such a problem, called a stability problem of the functional equation, was formulated by Ulam [1] in 1940. In the next year, Hyers [2] gave a partial solution of Ulam’s probl...

A familiar functional equation f(ax+b) = cf(x) will be solved in the class of functions f : R → R. Applying this result we will investigate the Hyers-Ulam-Rassias stability problem of the generalized additive Cauchy equation f ( a1x1+···+amxm+x0 )= m ∑ i=1 bif ( ai1x1+···+aimxm ) in connection with the question of Rassias and Tabor.

Using the Hyers-Ulam-Rassias stability method, weinvestigate isomorphisms in Banach algebras and derivations onBanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}Moreover, we prove the Hyers-Ulam-Rassias stability of homomorphismsin Banach algebras and of derivations on Banach ...

In this paper, we obtain the general solution and investigate the generalized Hyers-Ulam stability of the new generalized mixed type additive and quadratic functional equation in fuzzy normed space. Mathematics Subject Classification 39B55, 39B52, 39B82

‎Hensel [K‎. ‎Hensel‎, ‎Deutsch‎. ‎Math‎. ‎Verein‎, ‎{6} (1897), ‎83-88.] discovered the $p$-adic number as a‎ ‎number theoretical analogue of power series in complex analysis‎. ‎Fix ‎a prime number $p$‎. ‎for any nonzero rational number $x$‎, ‎there‎ ‎exists a unique integer $n_x inmathbb{Z}$ such that $x = ‎frac{a}{b}p^{n_x}$‎, ‎where $a$ and $b$ are integers not divisible by ‎$p$‎. ‎Then $|x...

using the hyers-ulam-rassias stability method, weinvestigate isomorphisms in banach algebras and derivations onbanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}moreover, we prove the hyers-ulam-rassias stability of homomorphismsin banach algebras and of derivations on banach ...