Black Hole Physics) with the prediction of a minimum measurable length [@new20; @new21; @new22; @new23; @new24; @new25; @new26; @new27; @new28; @new29]. Similar kind of commutation relation can also be found in the context of Polymer Quantization in terms of polymer mass scale [@new30]. Importance of the GUP can also be realized on the basis of simple gedanken experiments without any reference of a particular fundamental theory [@new27; @new28]. So we can think the GUP as a model independent concept, ideally perfect for the study of black hole entropy. The authors in [@new31] proposed a GUP which is consistent with DSR theory, string theory and black hole physics. This is approximately covariant under DSR transformations but not Lorentz covariant [@new29]. With the GUP as proposed by the authors in [@new31] we can arrive at the corrected entropy-area relation for a black hole which can be written in the following expansive form [@new37; @new]: $$\begin{aligned}
\label{ent}
S  ~\simeq & ~\frac{A}{4l_p^2} + a~ \sqrt{\frac{A}{4l_p^2}} + b~ \ln \left(\frac{A}{4l_p^2}\right) \nonumber \\
& + \sum_{m=\frac{1}{2},\frac{3}{2},\ldots}^\infty d_m  \left(\frac{A}{4l_p^2}\right)^{-m} + 
\sum_{n=1,2,\ldots}^\infty c_n  \left(\frac{A}{4l_p^2}\right)^{-n} + \mathit{const.} ~~.\end{aligned}$$ In this paper we will try to predict the form of $f(R)$ in holographic and new agegraphic DE models in the 