τ-CENTRALIZERS AND GENERALIZED DERIVATIONS

Generalized (σ , τ) higher derivations in prime rings

Let R be a ring and U be a Lie ideal of R. Suppose that σ, τ are endomorphisms of R. A family D = {d n } n ∈ N of additive mappings d n :R → R is said to be a (σ,τ)- higher derivation of U into R if d 0 = I R , the identity map on R and [Formula: see text] holds for all a, b ∈ U and for each n ∈ N. A family F = {f n } n ∈ N of additive mappings f n :R → R is said to be a generalized (σ,τ)- high...

Characterizations of centralizers and derivations on some algebras

A linear mapping φ on an algebra A is called a centralizable mapping at G ∈ A if φ(AB) = φ(A)B = Aφ(B) for each A and B in A with AB = G, and φ is called a derivable mapping at G ∈ A if φ(AB) = φ(A)B + Aφ(B) for each A and B in A with AB = G. A point G in A is called a full-centralizable point (resp. full-derivable point) if every centralizable (resp. derivable) mapping at G is a centralizer (r...

Generalized Derivations on Modules

Generalized Derivations on Modules *

Let A be a Banach algebra and M be a Banach left A-module. A linear map δ : M → M is called a generalized derivation if there exists a derivation d : A → A such that δ(ax) = aδ(x) + d(a)x (a ∈ A,x ∈ M). In this paper, we associate a triangular Banach algebra T to Banach A-module M and investigate the relation between generalized derivations on M and derivations on T . In particular, we prove th...

Nearly Generalized Jordan Derivations

Let A be an algebra and let X be an A-bimodule. A C−linear mapping d : A → X is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) δ : A → X such that d(a) = ad(a) + δ(a)a for all a ∈ A. The main purpose of this paper to prove the Hyers-Ulam-Rassias stability and superstability of the generalized Jordan derivations.