Polarization operator contributions to the Lamb shift and hyperfine splitting

We calculate radiative corrections to the Lamb shift of order alpha(3) (Zalpha)(5) m and radiative corrections to hyperfine splitting of order alpha(3)(Zalpha)E-F generated by the diagrams with insertions of <LF>radiative photons and electron polarization loops in the graphs with two external photons. We also obtain the radiative-recoil correction to hyperfine splitting in muonium generated by the diagrams with the tau polarization loop.