  In this paper we present the mass functions in the substellar regime of three
young open clusters, IC 348, $\sigma$ Orionis and Pleiades, as derived using
the data from the 2 Micron All Sky Survey (2MASS) catalogue which has a
limiting magnitude of K_s ~ 15, and the latest version of the Guide Star
Catalogue (GSC) which has a limiting magnitude of F ~ 21 where F refers to the
POSS II IIIa-F passband. Based on recent evolutionary models for low mass
stars, we have formulated the selection criteria for stars with masses below
0.5 solar mass. Using a statistical approach to correct for the background
contamination, we derive the mass function of objects with masses ranging from
0.5 solar mass down to the substellar domain, well below the Hydrogen Burning
Mass Limit. The lowest mass bins in our analysis are 0.025, 0.045 and 0.055
solar masses for IC 348, sigma Orionis and Pleiades, respectively. The
resultant slopes of the mass functions are 0.8 +/- 0.2 for IC 348, 1.2 +/- 0.2
for sigma Orionis and 0.5 +/- 0.2 for Pleiades, which are consistent with the
previous results. The contribution of objects below 0.5 solar mass to the total
mass of the cluster is ~40%, and the contribution of objects below 0.08 solar
mass to the total mass is ~4%.
