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We consider the Two Higgs Doublet Model (2HDM) of type III which leads to Flavour Changing Neutral Currents (FCNC) at tree level. In the framework of this model we can use an appropriate form of the Yukawa Lagrangian that makes the type II model limit of the general type III couplings apparent. This way is useful in order to compare with the experimental data which is model dependent. The analytical expressions of the partial width $\Gamma (t \to H^+ b) $ are derived and we compare with the data available at this energy range. We examine the limits on the new parameter $\lambda_{tt}$ from the validness criterium of perturbation theory and we get $\lambda_{tt} \geq \sqrt{2} (1-\tan \beta)/\sqrt{1+\tan^2 \beta}$. Furthermore, we analyze the perturbation theory limit together with experimental bounds on $B(t \to H^+ b)$ and we get a bound on the charged Higgs mass, $m_{H^+}\geq 123$ GeV

Bounds on the charged Higgs boson in the type III two Higgs doublet model from the Fermilab Tevatron