  Recently Ali et.al.(2009) proposed a Generalized Uncertainty Principle (or
GUP) with a linear term in momentum (accompanied by Plank length). Inspired by
this idea here we calculate the quantum corrected value of a Schwarzschild
black hole entropy and a Reissner-Nordstrom black hole with double horizon by
utilizing the proposed generalized uncertainty principle. We find that the
leading order correction goes with the square root of the horizon area
contributing positively. We also find that the prefactor of the logarithmic
contribution is negative and the value exactly matches with some earlier
existing calculations. With the Reissner-Nordstrom black hole we see that this
model independent procedure is not only valid for single horizon spacetime but
also valid for spacetimes with inner and outer horizons.
