  Using the Sharma-Mittal entropy, we study some properties of the
Schwarzschild and Schwarzschild-de Sitter black holes. The results are compared
with those obtained by attributing the Bekenstein entropy bound to the
mentioned black holes. Our main results show that while the Schwarzschild black
hole is always stable in the micro-canonical ensemble, it can be stable in the
canonical ensemble if its mass is bigger than the mass of the coldest
Schwarzschild black hole. A semi-classical analysis has also been used to find
an approximate relation between the entropy free parameters. Throughout the
paper, we use units $c=G=\hbar=k_B=1$, where $k_B$ denotes the Boltzmann
constant.
