  By Monte Carlo simulations we study critical properties of the mixed spin-1/2
and spin-1 Ising model on a triangular lattice, considering two different ways
of the spin-value distributions on the three sublattices: $(1/2,1/2,1)$ and
$(1/2,1,1)$. In the former case, we find standard Ising universality class
phase transitions between paramagnetic and magnetic phases but no phase
transitions between two distinct magnetic phases $(\pm 1/2,\pm 1/2,\pm 1)$ and
$(\pm 1/2,\pm 1/2,0)$ at any finite temperature, except for some interesting
non-critical anomalies displayed by response functions. On the other hand, the
latter case turns out to be a rare (or perhaps the only) example of a
two-dimensional mixed spin-1/2 and spin-1 Ising model on a standard lattice
that displays tricritical behavior.
