We consider a system consisting of a topological insulator with an array of magnetic adatoms interacting with the surface states of electrons. We find that the indirect coupling of the magnetic impurities results in a ferromagnetic ordering of the magnetic moments and is also responsible for the unusual linear dispersion of the surface magnons. We also show that the interaction of magnons with surface electrons essentially renormalizes the electron energy spectrum. The renormalized spectrum is nonlinear and can be characterized by a negative effective mass of electrons and holes for any k ≠ 0. The electron velocity near the Dirac point depends on the electron-magnon coupling.