Let \(\mathcal{N}\) be a~\(3\)-prime near ring and \(\alpha,\beta: \mathcal{N}\rightarrow \mathcal{N}\) be endomorphisms. In the present paper we amplify a~few outcomes concerning generalized derivations and two-sided \(\alpha\)-generalized derivations of \(3\)-prime near rings to generalized \((\alpha,\beta)\)-derivations. Cases demonstrating the need of the \(3\)-primeness speculation are given. When \(\beta = id_{\mathcal{N}}\) (resp. \(\alpha = \beta = id_{\mathcal{N}}\)), one can easily obtain the main results of~\cite{ref1} (resp.\cite{ref5}).

• 16N60 - Prime and semiprime associative rings
• 16W25 - Derivations, actions of Lie algebras
• 16Y30 - Near-rings

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