  In this paper, we study the relativistic correction to Bekenstein-Hawking
entropy in the canonical ensemble and isothermal-isobaric ensemble and apply it
to the cases of non-rotating BTZ and AdS-Schwarzschild black holes. This is
realized by generalizing the equations obtained using Boltzmann-Gibbs(BG)
statistics with its relativistic generalization, Kaniadakis statistics, or
$\kappa$-statistics. The relativistic corrections are found to be logarithmic
in nature and it is observed that their effect becomes appreciable in the
high-temperature limit suggesting that the entropy corrections must include
these relativistically corrected terms while taking the aforementioned limit.
The non-relativistic corrections are recovered in the $\kappa\rightarrow 0$
limit.
