  We study the critical behavior of a frustrated Blume-Capel (BC)
antiferromagnet on a triangular lattice by Monte Carlo simulations. For a
reduced single-ion anisotropy strength $-1.47 \lesssim d < 0$ we find two phase
transitions. The low-temperature phase is characterized by the
antiferromagnetic long-range ordering (LRO) on two sublattices with the third
one remaining in a non-magnetic state. At higher temperatures there is a
critical region of the Berezinskii-Kosterlitz-Thouless (BKT) type with a
power-law decaying spin-correlation function. For $-1.5 \le d \lesssim -1.47$,
there is only one phase transition from the LRO to the paramagnetic region and
the transition is of first order. The presence of the BKT phase in the current
frustrated BC model is a new feature not observed in its non-frustrated
counterparts. The values of the decay exponent $\eta$ of the BKT phase
corresponding to upper and lower temperatures appear to be consistent with the
theoretical predictions for the six-state clock model.
