  We consider a charged BTZ black hole in asymptotically AdS space-time of
massive gravity to study the effect of the thermal fluctuations on the black
hole thermodynamics. We consider the Einstein-Born-Infeld solution and
investigate critical points and stability. We also compare the results with the
case of Einstein-Maxwell solutions. Besides, we find that thermal fluctuations,
which appear as a logarithmic term in the entropy, affect the stability of the
black hole and change the phase transition point. Moreover, we study the
geometrical thermodynamics and find that the behaviour of the linear Maxwell
solution is the same as the nonlinear one.
