  Static black hole with the Power Maxwell invariant (PMI), Born-Infeld (BI),
logarithmic (LN), exponential (EN) electromagnetic fields in three-dimensional
spacetime with cosmological constant was studied. It was shown that the LN and
EN fields represent the Born-Infeld type of nonlinear electrodynamics. It the
framework of General Relativity the exact solutions of the field equations were
obtained, corresponding thermodynamic functions were calculated and the P-V
criticality of the black holes in the extended phase space thermodynamics was
investigated.
