  It is known from the early work of May in 1964 that ideal Bose gas do not
exhibit condensation phenomenon in two dimensions. On the other hand, it is
also known that the thermostatistics arising from q-deformed oscillator algebra
has no connection with the spatial dimensions of the system. Our recent work
concerns the study of important thermodynamic functions such as the entropy,
occupation number, internal energy and specific heat in ordinary three spatial
dimensions, where we established that such thermostatistics is developed by
consistently replacing the ordinary thermodynamic derivatives by the Jackson
derivatives. The thermostatistics of q-deformed bosons and fermions in two
spatial dimensions is an unresolved question and that is the subject of this
investigation. We study the principal thermodynamic functions of both bosons
and fermions in the two dimensional q-deformed formalism and we find that,
different from the standard case, the specific heat of q-boson and q-fermion
ideal gas, at fixed temperature and number of particle, are no longer
identical.
