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A one - dimensional iterative map with two control parameters, i.e. the Kim -Kong map, is proposed. Our purpose is to investigate the characteristicproperties of this map, and to discuss numerically the multifractal behavior ofthe normalized first passage time. Especially, based on the Monte Carlosimulation, the normalized first passage time to arrive at the absorbingbarrier after starting from an arbitrary site is mainly obtained in thepresence of both absorption and reflection on a two - dimensional Sierpinskigasket. We also discuss the multifractal spectra of the normalized firstpassage time, and the numerical result of the Kim - Kong model presented willbe compared with that of the Sinai and logistic models.

MULTIFRACTAL MEASURES CHARACTERIZED BY THE ITERATIVE MAP WITH TWO CONTROL PARAMETERS