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Phenomenology of lepton flavor violation in 2HDM(III) from (g-2)_mu and leptonic decays

We constrain some lepton flavor violating vertices in the context of the two Higgs doublet model type III, assuming that the lightest scalar Higgs mass $% m_{h^{0}} $is about $115 $GeV. Specifically, based on the $g-2 $muon factor and the decay width of$ μ\to eγ$,$ $the following quite general bounds are obtained:$ 7.62\times 10^{-4}\lesssim ξ_{μτ}^{2}\lesssim 4.44\times 10^{-2}, $ $ξ_{eτ}^{2}\lesssim 2.77\times 10^{-14}$. Additionally, based on the processes $τ\to μγ$, and $τ\to μμμ$, bounds on $ξ_{ττ} $and $ξ_{μμ} $are also gotten, such constraints on these parameters$ $still give enough room for either a strong suppression$ $or strong enhancement on the coupling of any Higgs boson to a pair of tau leptons or a pair of muons\textbf{.} Furthermore, upper limits on the decay widths of the leptonic decays $τ\to eγ, $and $τ\to eee $are calculated, finding them to stay far from the reach of near future experiments.