Let A be a Banach algebra, let σ be an automorphism of A, and let d, δ be q-skew σ-derivations of A. We show that if dδ(a) is quasi-nilpotent for any a∈A, then dδ(a)3 lies in the radical of A for all a∈A. This result simultaneously generalizes the previous results obtained by Brešar and Šemrl , Chebotar et al.  and Abdelali .
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics