Convergence speed for Fekete points on uniformly polynomially cuspidal sets

We obtain the convergence speed for Fekete points on uniformly polynomially cuspidal compact sets introduced by Pawłucki and Pleśniak. This is done by showing that these sets are \((\mathscr {C}^{\alpha }, \mathscr {C}^{\alpha '})\) $({\mathcal{C}}^{\alpha },{\mathcal{C}}^{{\alpha }^{\prime }})$ -regular in the sense of Dinh, Ma and Nguyen.