Current experimental data from the $g\ensuremath{-}2$ muon factor seem to show the necessity of physics beyond the standard model (SM), since the difference between SM and experimental predictions is approximately $2.6\ensuremath{\sigma}.$ In the framework of the general two Higgs doublet model, we calculate the muon anomalous magnetic moment to get lower and upper bounds for the flavor changing Yukawa couplings in the leptonic sector. We also obtain lower bounds for the mass of the Higgs pseudoscalar ${(m}_{{A}^{0}})$ as a function of the parameters of the model.