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The lepton flavor violating decays $h\to e_b^\pm e_a^\mp $, $Z\to e_b^\pme_a^\mp$, and $e_b\to e_a \gamma$ will be discussed in the framework of the TwoHiggs doublet model with presence of new inverse seesaw neutrinos and a singlycharged Higgs boson that accommodate both $1\sigma$ experimental data of$(g-2)$ anomalies of the muon and electron. Numerical results indicate thatthere exist regions of the parameter space supporting all experimental data of$(g-2)_{e,\mu}$ as well as the promising LFV signals corresponding to thefuture experimental sensitivities.

$(g-2)_{e,\mu}$ anomalies and decays $h\to e_a e_b$, $Z\to e_ae_b$, and  $e_b\to e_a \gamma$ in a two Higgs doublet model with inverse seesaw  neutrinos