  In (2+1) dimensions, we consider the model of a $N$ flavor, two-component
fermionic field interacting through a Chern-Simons field besides a four fermion
self-interaction which consists of a linear combination of the Gross-Neveu and
Thirring like terms. The four fermion interaction is not perturbatively
renormalizable and the model is taken as an effective field theory in the
region of low momenta. Using Zimmerman procedure for reducing coupling
constants, it is verified that, for small values of the Chern-Simons parameter,
the origin is an infrared stable fixed point but changes to ultraviolet stable
as $\alpha$ becomes bigger than a critical $\alpha_c$. Composite operators are
also analyzed and it is shown that a specific four fermion interaction has an
improved ultraviolet behavior as $N$ increases.
