Relative Rota-Baxter operators on a Jordan algebra with a representation and related structures

The purpose of this paper is to study O-(dual-) Nijenhuis structures on a Jordan algebra with a representation. The notion of a (dual-)Nijenhuis pair is introduced and it can generate a trivial deformation of a Jordan algebra with representation. We introduce the notion of a O-(dual-)Nijenhuis structure on a Jordan algebra with representation. Furthermore, we verify that relative Rota-Baxter operators and O-(dual)Nijenhuis structures can give rise to each other under some conditions. Finally, we study the notions of Rota-Baxter-Nijenhuis structures, r-matrix-Nijenhuis structures, N-structures on a Jordan algebra and we investigate the relation between them.