  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.
