  In this work, we shall analyze the effects of quantum fluctuations on the
properties of a BTZ black hole, in a massive theory of gravity. We will analyze
this for a charged BTZ black hole in asymptotically AdS and dS space-times. The
quantum fluctuations would produce thermal fluctuations in the thermodynamics
of this BTZ black hole. As these fluctuations would become relevant at a
sufficiently small scale, we shall discuss the effects of such thermal
fluctuations on the entropy of a small charged BTZ black. We shall also analyze
the effects of these fluctuations on the stability of such a black hole.
