  The generalized uncertainty principle (GUP) corrected modified relativistic
particle model has been derived in curved space-time. From this modified model,
the equation of motion (EM) has been constructed relativistically in terms of
the affine parameter ($\lambda$) or proper time ($\tau$) and
nonrelativistically in terms of coordinate time ($t$). In this context, the
constraint analysis technique has been applied to get the EM. Interestingly,
the EM obtained in both cases is the usual one. This result clearly indicates
an important fact, that is, consistency of the equivalence principle in the GUP
framework, and furthermore it can be concluded that with the GUP-corrected
modified algebra it is impossible to get the GUP effect in point particle
motion.
