In this paper, we study Hyers–Ulam and generalized Hyers–Ulam–Rassias stability of a system hyperbolic partial differential equations using Gronwall’s lemma Perov’s theorem.

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 ...

Recently the generalizedHyers-Ulam orHyers-Ulam-Rassias stability of the following functional equation ∑m j 1 f −rjxj ∑ 1≤i≤m,i / j rixi 2 ∑m i 1 rif xi mf ∑m i 1 rixi where r1, . . . , rm ∈ R, proved in Banach modules over a unital C∗-algebra. It was shown that if ∑m i 1 ri / 0, ri, rj / 0 for some 1 ≤ i < j ≤ m and a mapping f : X → Y satisfies the above mentioned functional equation then the...

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

The object of this paper is to determine Hyers–Ulam–Rassias stability concerning the Jensen functional equation in intuitionistic fuzzy normed space (IFNS) by using the fixed point method. Further, we establish stability of the Cauchy functional equation in IFNS.

In the present paper a certain form of the Hyers–Ulam stability of monomial functional equations is studied. This kind of stability was investigated in the case of additive functions by Th. M. Rassias and Z. Gajda.

In this paper, we prove the Hyers–Ulam–Rassias stability of the quadratic mapping in generalized quasi-Banach spaces, and of the quadratic mapping in generalized p-Banach spaces.

In this paper, we investigate the generalized Hyers-Ulam-Rassias stability of a new quadratic functional equation f (2x y) 4f (x) f (y) f (x y) f (x y) + = + + + − −

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.

The Hyers-Ulam stability, the Hyers-Ulam-Rassias stability, and also the stability in the spirit of Gǎvru̧ta for each of the following quadratic functional equations f(x+y)+ f(x−y) = 2f(x)+ 2f(y), f(x+y + z)+ f(x−y)+ f(y − z)+ f(z−x) = 3f(x)+3f(y)+3f(z), f (x+y+z)+f(x)+f(y)+f(z)= f(x+y)+f(y+z)+f(z+x) are investigated. 2000 Mathematics Subject Classification. Primary 39B52, 39B72, 39B82.