  In this paper, by using Verlinde's formalism and a modified Padmanabhan's
prescription, we have obtained the lowest order quantum correction to the
gravitational acceleration and MOND-type theory by considering a nonzero
difference between the number of bits of the holographic screen and the number
of bits of the holographic screen that satisfy the equipartition theorem (the
bulk). We will also carry out an analysis for the pure and an asymptotic
(actual) de Sitter Universe considering the holographic principle. We had also
used nonextensive concepts into the theory and we accomplished a
$N$-dimensional generalization of our results. Some physical consequences of
the nonextensive ideas in Gauss-Bonnet (GB) gravity theory were analyzed also.
We have obtained the $q$-parameter as a function of the GB coefficient and some
physical aspects were discussed.
