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In this paper, we investigate the influences of two continuum radiationpressures of the central engines on the black hole mass estimates for 40 activegalactic nuclei (AGNs) with high accretion rates. The two continuum radiationpressure forces, usually believed negligible or not considered, are from thefree electron Thomson scattering, and the recombination and re-ionization ofhydrogen ions that continue to absorb ionizing photons to compensate for therecombination. The masses counteracted by the two radiation pressures$M_{\rm{RP}}$ depend sensitively on the percent of ionized hydrogen in theclouds $\beta$, and are not ignorable compared to the black hole virial masses$M_{\rm{RM}}$, estimated from the reverberation mapping method, for these AGNs.As $\beta$ increases, $M_{\rm{RP}}$ also does. The black hole masses$M_{\rm{\bullet}}$ could be underestimated at least by a factor of 30--40percent for some AGNs accreting around the Eddington limit, regardless ofredshifts of sources $z$. Some AGNs at $z < 0.3$ and quasars at $z \ga 6.0$have the same behaviors in the plots of $M_{\rm{RP}}$ versus $M_{\rm{RM}}$. Thecomplete radiation pressures will be added as AGNs match $M_{\rm{RP}}\ga 0.3M_{\rm{RM}}$ due to the two continuum radiation pressures. Compared to$M_{\rm{RM}}$, $M_{\rm{\bullet}}$ might be extremely underestimated ifconsidering the complete radiation pressures for the AGNs accreting around theEddington limit.

Influences of Radiation Pressures on Mass Estimates of Supermassive Black Holes in AGNs