  As a generalized uncertainty principle (GUP) leads to the effects of the
minimal length of the order of the Planck scale and UV/IR mixing, some
significant physical concepts and quantities are modified or corrected
correspondingly. On the one hand, we derive the maximally localized states ---
the physical states displaying the minimal length uncertainty associated with a
new GUP proposed in our previous work. On the other hand, in the framework of
this new GUP we calculate quantum corrections to the thermodynamic quantities
of the Schwardzschild black hole, such as the Hawking temperature, the entropy,
and the heat capacity, and give a remnant mass of the black hole at the end of
the evaporation process. Moreover, we compare our results with that obtained in
the frameworks of several other GUPs. In particular, we observe a significant
difference between the situations with and without the consideration of the
UV/IR mixing effect in the quantum corrections to the evaporation rate and the
decay time. That is, the decay time can greatly be prolonged in the former
case, which implies that the quantum correction from the UV/IR mixing effect
may give rise to a radical rather than a tiny influence to the Hawking
radiation.
