Three-loop radiative-recoil corrections to hyperfine splitting generated by one-loop fermion factors

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by diagrams with one-loop radiative photon insertions both in the electron and muon lines. An analytic result for these nonlogarithmic corrections of order alpha(Z(2)alpha)(Zalpha)(m/M)E-F is obtained. This result constitutes a next step in the implementation of the program of reduction of the theoretical uncertainty of hyperfine splitting below 10 Hz.