The generalized Hyers-Ulam-Rassias stability of generalized derivations on unital Banach algebras into Banach bimodules is established. ∗2000 Mathematics Subject Classification. Primary 39B82; Secondary 46H25, 39B52, 47B47.

In this paper, the author established the general solution and generalized Ulam Hyers Rassias stability of n− dimensional Arun-additive functional equation f ( nx0 ± n ∑

‎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, ‎using fixed point method‎, ‎we prove the generalized hyers-ulam stability of‎ ‎random homomorphisms in random $c^*$-algebras and random lie $c^*$-algebras‎ ‎and of derivations on non-archimedean random c$^*$-algebras and non-archimedean random lie c$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...

In this paper we establish Hyers-Ulam-Rassias stability of a generalized functional equation in fuzzy Banach spaces. The concept originated from Th. M. Rassias theorem that appeared his paper: On the linear mapping spaces, Proc. Amer. Math. Soc. 72 (1978), 297-30.

Under what conditions does there exist a group homomorphism near an approximate group homomorphism? This question concerning the stability of group homomorphisms was posed by Ulam 1 . The case of approximately additive mappings was solved by Hyers 2 on Banach spaces. In 1950 Aoki 3 provided a generalization of the Hyers’ theorem for additive mappings and in 1978 Th. M. Rassias 4 generalized the...

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.

The question concerning the stability of group homomorphisms was posed by Ulam 1 . Hyers 2 solved the case of approximately additive mappings on Banach spaces. Aoki 3 provided a generalization of the Hyers’ theorem for additive mappings. In 4 , Rassias generalized the result of Hyers for linear mappings by allowing the Cauchy difference to be unbounded see also 5 . The result of Rassias has bee...

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) + = + + + − −

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.