The numerical calculations of the screened vacuum-polarization corrections are performed in coordinate space employing the finite basis set constructedfrom the DKB-splines [54]. For the electric-loop potential U el $_{VP}$, that enters Δ E VP( A ) SQED , Δ E VP( B ) SQED , Δ E VP( E ) SQED , and Δ E VP( G ) SQED , we employ the well-known expression for the Uehling part and the approximate formulas from Ref. [59] for the Wichmann-Kroll part. The magnetic-loop potential U ml VP ( Δ E VP( C ) SQED and Δ E VP( H ) SQED ) is taken in the Uehling approximation only. In case of the g factor this leads to zero contribution. In case of the hyperfine structure we use the expression for the e xtended nucleus from Ref. [47]. For the operator I$_{VP}$ ( Δ E VP( F ) SQED and Δ E VP( I ) $_{SQED}$) we also employ the Uehling approximation, the corresponding expressions are taken from Ref. [58]. The calculational procedure has been checked utilizing the Feynman and Coulomb gauges for the photon propagator mediating the interelectronic interaction. The results in both gauges are presented term by term in Tables I and II for the g factor of $^{208}$Pb 79+ and for the hyperfine splitting of $^{209}$Bi $^{83+}$, respectively. The total value of the g factor of a Li-like ion can be written as Here g$_{D}$ is the Dirac value, Δ g$_{int}$ is the interelectronic-interaction correction, Δ g$_{QED}$ is the one- electron QED correction, Δ g$_{SQED}$ is the screened QED correction, and Δ g$_{nuc}$ is the contribution of nuclear effects (finite nuclear size, nuclear recoil and n uclear polarization). To the first order in α and 1 /Z the screened QED correction is defined by the set of the two-el ectron QED diagrams evaluated in the present paper. The operator T$_{0}$ in this case reads V. RESULTS AND DISCUSSION A. g factor g = g$_{D}$ + Δ g$_{int}$ + Δ g$_{QED}$ + Δ g$_{SQED}$ + Δ g$_{nuc}$ . (67) T$_{0}$ = µ$_{0}$ [ r × α ] · H , (68) Δ g$_{SQED}$ = Δ g SE SQED + Δ g VP $_{SQED}$, (69) Δ g SE / VP SQED = Δ E SE / VP SQED / ( µ$_{0}$ H m$_{j}$ ) , (70) 16 where µ$_{0}$ = | e | / 2 is the Bohr magneton, $^{H}$is the magnetic field directed along the z -axis. The corresponding contribution to the g factor is given by