  A new relativity theory, or more concretely an extended relativity theory,
actively developed by one of the authors incorporates 3 basic concepts. They
are the old idea of Chew about bootstrapping, Nottale's scale relativity, and
enlargement of the conventional time-space by inclusion of noncommutative
Clifford manifolds where all p-branes are treated on equal footing. The latter
allows one to write a master action functional. The resulting functional
equation is simplified and applied to the p-loop oscillator. Its solution
represents a generalization of the conventional quantum point oscillator. In
addition, it exhibits some novel features: an emergence of two explicit scales
delineating the asymptotic regimes (Planck scale region and a smooth region of
a quantum point oscillator). In the most interesting Planck scale regime, the
solution recovers in an elementary fashion some basic relations of string
theory (including string tension quantization and string uncertainty relation).
It is shown that the degeneracy of the $first$ collective excited state of the
p-loop oscillator yields not only the well-known Bekenstein-Hawking
area-entropy linear relation but also the logarithmic corrections therein. In
addition we obtain for any number of dimensions the Hawking temperature, the
Schwarschild radius, and the inequalities governing the area of a black hole
formed in a fusion of two black holes. One of the interesting results is a
demonstration that the evaporation of a black hole is limited by the upper
bound on its temperature, the Planck temperature.
