  Our primary goal in this paper is to confirm new universal relations in black
hole thermodynamics. We investigate the universal relations by selecting
different black holes. First, we obtain the black holes' thermodynamic
relations assuming a new minor correction is added to the AdS part of the
action. Then we confirm the universal relations by performing a series of
direct calculations. It is noteworthy that according to each of the properties
related to black holes, a new universal relation can be obtained according to
this method. We confirm two different types of these universal relations for
various block holes. Furthermore, we also consider black holes in AdS space
surrounded by perfect fluid. We use the small correction to the action and
obtain the modified thermodynamic quantities. We achieve two new universal
relations which correspond to the parameters of perfect fluid and magnetic
charge of the Bardeen AdS Black Hole. Finally, the new universal relation leads
us to understand the charge-to-mass ratio, i.e., WGC-like behavior. We also
find that the weak gravity conjecture condition is satisfied for the black hole
surrounded by perfect fluid.
