Abstract
In this paper, we study entropy relations and bounds of regular and singular black holes with nonlinear electrodynamics sources. We focus on the regular and singular Bardeen and Hayward black holes in asymptotically flat and AdS spacetimes. For black holes with vanishing effective mass , it is found that the entropy product is always mass-independent in asymptotically flat spacetime, while the entropy sum takes the mass-independent universality in asymptotically AdS spacetime. For the cases with nonzero effective mass in asymptotically flat and AdS spacetimes, entropy relations are both some functions of mass and charge, hence are always mass-dependent. Besides, the non-linear electrodynamics always affects the entropy bounds of horizons.
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