  Based on mean field calculations with Skyrme interactions, we extract a
constraint on the isovector effective mass in nuclear matter at saturation
density $\rho_0$, i.e., $m_{v}^{\ast}(\rho_0)=(0.77\pm0.03) m$ by combining the
experimental data of the centroid energy of the isovector giant dipole
resonance (IVGDR) and the electric dipole polarizability $\alpha_{\mathrm{D}}$
in $^{208}$Pb. Meanwhile, the isoscalar effective mass at $\rho_0$ is
determined to be $m_{s}^{\ast}(\rho_0)=(0.91\pm0.05) m$ by analyzing the
measured excitation energy of the isoscalar giant quadrupole resonance (ISGQR)
in $^{208}$Pb. From the constrained $m_{s}^{\ast}(\rho_0)$ and
$m_{v}^{\ast}(\rho_0)$, we obtain the isospin splitting of nucleon effective
mass in asymmetric nuclear matter of isospin asymmetry $\delta$ at $\rho_0$ as
$[m_n^{\ast}(\rho_0,\delta)-m_p^{\ast}(\rho_0,\delta)]/m = \Delta m^*_1(\rho_0)
\delta + O(\delta^3)$ with the linear isospin splitting coefficient $\Delta
m^*_1(\rho_0) = 0.33\pm0.16$. We notice that using the recently corrected data
on the $\alpha_{\mathrm{D}}$ in $^{208}$Pb with the contribution of the
quasideuteron effect subtracted slightly enhances the isovector effective mass
to $m_{v}^{\ast}(\rho_0)=(0.80\pm0.03) m$ and reduces the linear isospin
splitting coefficient to $\Delta m^*_1(\rho_0) = 0.27\pm0.15$. Furthermore, the
constraints on $m_{v}^{\ast}(\rho)$, $m_{s}^{\ast}(\rho)$ and $\Delta
m^*_1(\rho)$ at other densities are obtained from the similar analyses and we
find that the $\Delta m^*_1(\rho)$ increases with the density.
