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.

Let W be a simple generalized Witt algebras over a field of characteristic zero. In this paper, it is proved that each anti-symmetric biderivation of W is inner. As an application of biderivations, it is shown that a linear map ψ on W is commuting if and only if ψ is a scalar multiplication map on W. The commuting automorphisms and derivations of W are determined.

we show that  higher derivations on a hilbert$c^{*}-$module associated with the cauchy functional equation satisfying generalized hyers--ulam stability.

We show that it is algebraically consistent to express the string field theory operators ∂, K and I as inner derivations of the B-V algebra of string vertices. In this approach, the recursion relations for the string vertices are found to take the form of a ‘geometrical’ quantum master equation, 1 2{B,B} + ∆B = 0. We also show that the B-V delta operator cannot be an inner derivation on the alg...

The main purpose of this research is to characterize generalized (left) derivations and Jordan (*,*)-derivations on Banach algebras rings using some functional identities. Let A be a unital semiprime algebra let F,G : ? linear mappings satisfying F(x) =-x2G(x-1) for all x Inv(A), where Inv(A) denotes the set invertible elements A. Then both F G are Another result in regard as follows. n > 1 ...