  We report first results from a large project to measure black hole (BH) mass
in high accretion rate active galactic nuclei (AGNs). Such objects may be
different from other AGNs in being powered by slim accretion disks and showing
saturated accretion luminosities, but both are not yet fully understood. The
results are part of a large reverberation mapping (RM) campaign using the 2.4-m
Shangri-La telescope at the Yunnan Observatory in China. The goals are to
investigate the gas distribution near the BH and the properties of the central
accretion disks, to measure BH mass and Eddington ratios, and to test the
feasibility of using such objects as a new type of cosmological candles. The
paper presents results for three objects, Mrk 335, Mrk 142 and IRAS F12397+3333
with H$\beta$ time lags relative to the 5100\AA\ continuum of
$10.6^{+1.7}_{-2.9}$, $6.4^{+0.8}_{-2.2}$ and $11.4^{+2.9}_{-1.9}$ days,
respectively. The corresponding BH masses are $(8.3_{-3.2}^{+2.6})\times
10^6M_{\odot}$, $(3.4_{-1.2}^{+0.5})\times 10^6M_{\odot}$ and
$(7.5_{-4.1}^{+4.3})\times 10^6M_{\odot}$, and the lower limits on the
Eddington ratios 0.6, 2.3, and 4.6 for the minimal radiative efficiency of
0.038. Mrk 142 and IRAS F12397+333 (extinction corrected) clearly deviate from
the currently known relation between H$\beta$ lag and continuum luminosity. The
three Eddington ratios are beyond the values expected in thin accretion disks
and two of them are the largest measured so far among objects with RM-based BH
masses. We briefly discuss implications for slim disks, BH growth and
cosmology.
