Summary: Recently, the Heisenberg’s uncertainty principle has been extended to incorporate the existence of a large (cut-off) length scale in de Sitter or anti-de Sitter space, and the Hawking temperatures of the Schwarzshild-(anti) de Sitter black holes have been reproduced by using the extended uncertainty principle. I generalize the extended uncertainty to the case with an absolute minimum length and compute its modification to the Hawking temperature. I obtain a general trend that the generalized uncertainty principle due to the absolute minimum length “always” increases the Hawking temperature, implying “faster” decay, which is in conformity with the result in the asymptotically flat space. I also revisit the black hole-string phase transition, in the context of the generalized uncertainty principle.