  Two-loop QED corrections with closed fermion loops are calculated for the 1s
bound-electron g factor. Calculations are performed to all orders in the
nuclear binding strength parameter Z\alpha (where Z is the nuclear charge and
\alpha is the fine structure constant) except for the closed fermion loop,
which is treated within the free-loop (Uehling) approximation in some cases.
Comparison with previous Z\alpha-expansion calculations is made and the
higher-order remainder of order \alpha^2(Z\alpha)^5 and higher is separated out
from the numerical results.
