  We calculate three-loop radiative-recoil corrections to hyperfine splitting
in muonium generated by the diagrams with the first order electron and muon
polarization loop insertions in graphs with two exchanged photons. These
corrections are enhanced by the large logarithm of the electron-muon mass
ratio. The leading logarithm squared contribution was obtained a long time ago.
Here we calculate the single-logarithmic and nonlogarithmic contributions. We
previously calculated the three-loop radiative-recoil corrections generated by
two-loop polarization insertions in the exchanged photons. The current paper
therefore concludes calculation of all three-loop radiative-recoil corrections
to hyperfine splitting in muonium generated by diagrams with closed fermion
loop insertions in the exchanged photons. The new results obtained here improve
the theory of hyperfine splitting, and affect the value of the electron-muon
mass ratio extracted from experimental data on the muonium hyperfine splitting.
