In this paper, we introduce a new class of generalized derivations on multiplicative Hom-Lie algebras, called G-αk-derivations. Such derivations depend on two automorphisms θ,ϑ∈G and generalize the classical αk-derivations of original algebras. We construct a nontrivial Hom-Lie algebra and its (θ,id)-αk-derivations following a geometric progression rule. Moreover, we prove that two related derivation spaces share the same dimension. Particularly, a Hom-Lie algebra structure is constructed on the direct sum of derivations and θ-derivations. Finally, we study the restriction of G-αk-derivations to Hom-ideals and establish their relationships with αk-quasi-derivations.
Li et al. (Wed,) studied this question.
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