J an 2 00 5 Hyers – Ulam – Rassias Stability of Generalized Derivations ∗
نویسنده
چکیده
The generalized Hyers–Ulam–Rassias stability of generalized derivations on unital normed algebras into Banach bimodules is established. ∗2000 Mathematics Subject Classification. Primary 39B82; Secondary 46H25, 39B52, 47B47.
منابع مشابه
Fixed point approach to the Hyers-Ulam-Rassias approximation of homomorphisms and derivations on Non-Archimedean random Lie $C^*$-algebras
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: $$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...
متن کاملm at h . FA ] 2 5 Fe b 20 05 Hyers - Ulam - Rassias Stability of Generalized Derivations ∗
The generalized Hyers-Ulam-Rassias stability of generalized derivations on unital Banach algebras into Banach bimodules is established. ∗2000 Mathematics Subject Classification. Primary 39B82; Secondary 46H25, 39B52, 47B47.
متن کاملApproximate solutions of homomorphisms and derivations of the generalized Cauchy-Jensen functional equation in $C^*$-ternary algebras
In this paper, we prove Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$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...
متن کاملOn the stability of generalized derivations on Banach algebras
We investigate the stability of generalizedderivations on Banach algebras with a bounded central approximateidentity. We show that every approximate generalized derivation inthe sense of Rassias, is an exact generalized derivation. Also thestability problem of generalized derivations on the faithful Banachalgebras is investigated.
متن کاملGeneralized additive functional inequalities in Banach algebras
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 ...
متن کامل