1. A. H. Sales, About K-Fibonacci numbers and their associated numbers; Int. J. of Math Forum, Vol. 6, no.50, (2011) 24732479. 2. D. H. Hyers, On the stability if linear functional equation, Proc. Natl. Acad. Sci. USA. 27(1941) 221-224. 3. D. H. Hyers, G. Isac and Th. M Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Boston, 1998. 4. D. H. Hyers and Th. M. Rassias, ...

In this paper we present four types of Ulam stability for ordinary differential equations: Ulam-Hyers stability, generalized UlamHyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-HyersRassias stability. Some examples and counterexamples are given.

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.

in the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{e}$$ isgiven where $sigma$ is an involution of the normed space $e$ and$k$ is a fixed positive integer. furthermore we investigate thehyers-ulam-rassias stability of the functional equation. thehyers-ulam stability on unbounded domains is also studied.applic...

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 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 Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$eta mu fleft(frac{x+y}{eta}+zright) = f(mu x) + f(mu y) +eta f(mu z)$$ for all $mu in mathbb{S}:= { lambda in mathbb{C} : |lambda | =1}$ and for any fixed positive integer $eta geq 2$ on $C^*$-ternary algebras by using fixed poind alternat...

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

In 1940, Ulam [13] proposed the Ulam stability problem of additive mappings. In the next year, Hyers [5] considered the case of approximately additive mappings f : E→ E′, where E and E′ are Banach spaces and f satisfies inequality ‖ f (x+ y)− f (x)− f (y)‖ ≤ ε for all x, y ∈ E. It was shown that the limit L(x) = limn→∞ 2−n f (2nx) exists for all x ∈ E and that L is the unique additive mapping s...

Let X,Y be complex vector spaces. Recently, Park and Th.M. Rassias showed that if a mapping f : X → Y satisfies f(x+ iy) + f(x− iy) = 2f(x)− 2f(y) (1) for all x, y ∈ X, then the mapping f : X → Y satisfies f(x+ y) + f(x− y) = 2f(x) + 2f(y) for all x, y ∈ X. Furthermore, they proved the generalized Hyers-Ulam stability of the functional equation (1) in complex Banach spaces. In this paper, we wi...