  The links between the deformation parameter $\beta$ of the generalized
uncertainty principle (GUP) to the two free parameters $\hat{\omega}$ and
$\gamma$ of the running Newtonian coupling constant of the Asymptotic Safe
gravity (ASG) program, has been conducted recently in [Phys.Rev.D 105 (2022)
12, 124054]. In this paper, we test these findings by calculating and examining
the shadow and quasinormal modes of black holes and demonstrate that the
approach provides a theoretical framework for exploring the interplay between
quantum gravity and GUP. Our results confirm the consistency of ASG and GUP and
offer new insights into the nature of black holes and their signatures. The
implications of these findings for future studies in quantum gravity are also
discussed.

General Relativity and Quantum Cosmology