The reseach of corrections to the fine shift of energy levels in the hydrogen-like atoms

The method of calculation of the value the thin shifts of energy levels of bound states on a basis relativistic upgraded quasipotential equation is considered. The appropriate perturbation theory permitting to calculate shifts of the energy levels in hydrogen-like atoms with a high accuracy is advanced. We obtained logarithmic corrections about $\alpha^6\ln\alpha^{-1}$ by one photon interaction are obtained, and earlier conventional result is confirmed.