  We first use the coherent state formalism of fuzzy space to show that the
fuzziness will eliminate point-like structure of a particle in favor of smeared
object, which is an exponential decay function in contrast to the Gaussian type
in the Moyal noncommutative space. The exponential decay function implies that,
in the UV region, the fuzziness provides an extra power-decay factor in the
Feynman propagator, contrasts to the exponential-decay factor in the Moyal
space. We also calculate the particle heat capacity and see that it approaches
to zero at high temperature. Next, we use the found smeared source to study the
Schwarzschild-like geometry and see that the black hole can reach a finite
maximum temperature before cooling down to absolute zero and leave a stable
remnant, as that in the noncommutative case. The properties of fuzzy 3D BTZ and
the fuzzy Kaluza-Klein black holes are also discussed. Finally, we present a
criterion for existence a regular black hole with a general smeared source
function.
