  We study the generalization of the mass function of classes of regular
spherically symmetric black holes solutions of in $ 4D $ coming from the
coupling of General Relativity with Non-linear Electrodynamics, through the
requirement of the energy conditions. Imposing that the solution must be
regular and that the Weak and Dominant Energy Conditions are simultaneously
satisfied, for models with the symmetry $T^0_{\;\;0} = T^1_{\;\;1} $ of the
tensor energy-momentum, we construct a new general class of regular black holes
of which two cases are asymptotically Reissner-Nordstrom.
