  Entropic uncertainty relations for the position and momentum within the
generalized uncertainty principle are examined. Studies of this principle are
motivated by the existence of a minimal observable length. Then the position
and momentum operators satisfy the modified commutation relation, for which
more than one algebraic representation is known. One of them is described by
auxiliary momentum so that the momentum and coordinate wave functions are
connected by the Fourier transform. However, the probability density functions
of the physically true and auxiliary momenta are different. As the
corresponding entropies differ, known entropic uncertainty relations are
changed. Using differential Shannon entropies, we give a state-dependent
formulation with correction term. State-independent uncertainty relations are
obtained in terms of the R\'{e}nyi entropies and the Tsallis entropies with
binning. Such relations allow one to take into account a finiteness of
measurement resolution.
