Abstract
The goal of this work is to introduce the notion of 3-Hom-L-dendriform algebras which is the dendriform version of 3-Hom-Lie-algebras. They can be also regarded as the ternary analogous of Hom-L-dendriform algebras. We give the representation of a 3-Hom-pre-Lie algebra. Moreover, we introduce the notion of Nijenhuis operators on a 3-Hom-pre-Lie algebra and provide some constructions of 3-Hom-L-dendriform algebras in term of Nijenhuis operators. Parallelly, we introduce the notion of a product and complex structures on a 3-Hom-L-dendriform algebras and there are also four types special integrability conditions.