(untitled) (European Journal of Pure and Applied Mathematics, 2025)
The paper investigates nonadditive mappings \(Ω: → \) on a prime ring \(\) with involution \( * \), characterized by satisfying one of the following conditions: enumerate \( [Ω(u), Ω(v)]_= [u, v]_\) for all \( u, v \). \( [Ω(u), v]_= [u, Ω(v)]_\) for all \( u, v \). \( Ω(u v) = Ω(u) v \) for all \( u, v \). enumerate Furthermore, the paper characterizes generalized bi-skew Jordan derivations within prime \( * \)-rings and examines the implications of these results in the context of various operator algebras.