2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/192589We introduce a magnetically charged extremal regular black hole in the coupled system of Einstein gravity and nonlinear electrodynamics. Its near horizon geometry is given by $AdS_2\times S^2$. It turns out that the entropy function approach does not automatically lead to a correct entropy of the Bekenstein-Hawking entropy. This contrasts to the case of the extremal Reissner-Norström black hole in the Einstein-Maxwell theory. We conclude that the entropy function approach does not work for a magnetically charged extremal regular black hole without singularity, because of the nonlinearity of the entropy function.17 Pages, 4 figures, version to appear in Phys. Lett. BGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext