  In this paper we have shown that the connection between the number of bits
and the area of the holographic screen, where both were established in
Verlinde's theory of entropic gravity, may depend on the thermostatistics
theory previously chosen. Starting from the Boltzmann-Gibbs (BG) theory, we
have reobtained the usual dependency of both, bits number and area. After that,
using Tsallis' entropy concept within the entropic gravity formalism, we have
derived another relation between the bits number and the holographic screen
area. Moreover, we have used this new relation to derive three Newtonian-type
accelerations in the context of Tsallis' statistics. Moreover, we have used
this new relation to derive three Newtonian-type acceleration in the context of
Tsallis statistics which are a modified gravitational acceleration, a modified
MOND theory and a modified Friedmann equation. We have obtained the
nonextensive version of the Tully-Fisher (TF) relation which shows a dependency
of the distance of the star in contrast to the standard TF expression. The BG
limit gives the standard TF law.
