Weighted $\mathcal{O}$-operators on Hom-Lie triple systems

In this paper, we first introduce the notion of a weighted $\mathcal{O}$-operator on Hom-Lie triple systems with respect to an action on another Hom-Lie triple system. Next, we construct a cohomology of weighted $\mathcal{O}$-operator on Hom-Lie triple systems, we use the first cohomology group to classify linear deformations and we investigate the obstruction class of an extendable $n$-order deformation. We end this paper by introducing a new algebraic structure, in connection with weighted $\mathcal{O}$-operators, called Hom-post-Lie triple system. We further show that Hom-post-Lie triple systems can be derived from Hom-post-Lie algebras.