Generalized (α, β)-derivations in 3-prime near-rings

Abstract

Let be a 3-prime near-ring and are endomorphisms. In this paper, we generalize a few results concerning generalized derivations and two sided α -generalized derivations of 3-prime near rings to generalized (α, β) -derivations. Cases demonstrating the need of the 3-primeness speculation is given. When (resp. ), one can easily obtain the main results of [1] (resp. [4]).