  A one - dimensional iterative map with two control parameters, i.e. the Kim -
Kong map, is proposed. Our purpose is to investigate the characteristic
properties of this map, and to discuss numerically the multifractal behavior of
the normalized first passage time. Especially, based on the Monte Carlo
simulation, the normalized first passage time to arrive at the absorbing
barrier after starting from an arbitrary site is mainly obtained in the
presence of both absorption and reflection on a two - dimensional Sierpinski
gasket. We also discuss the multifractal spectra of the normalized first
passage time, and the numerical result of the Kim - Kong model presented will
be compared with that of the Sinai and logistic models.
