Characterizations of Nonadditive Mappings in Prime $*$-Rings Involving Bi-Skew Products (European Journal of Pure and Applied Mathematics, 2025)
The paper investigates nonadditive mappings \(\Omega: \Re \to \Re\) on a prime ring \(\Re\) with involution \( * \), characterized by satisfying one of the following conditions:    \begin{enumerate}        \item  \( [\Omega(u), \Omega(v)]_\bullet = [u, v]_\bullet \) for all \( u, v \in \Re \).        \item  \( [\Omega(u), v]_\bullet = [u, \Omega(v)]_\bullet \) for all \( u, v \in \Re \).        \item  \( \Omega(u \bullet v) = \Omega(u) \bullet v \) for all \( u, v \in \Re \).    \end{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.