  Black hole solutions to the Einstein equations coupled with the Born--Infeld
electromagnetism associated with generalized nonlinear electrodynamics,
carrying both electric and magnetic charges, often referred to as dyonically
charged black holes, of finite energies, are constructed. These solutions give
rise to relegated curvature singularities at the center of the matter sources
of the black holes and approach the classical Reissner--Nordstrom black hole
asymptotically.
