Weak MPCEP and *CEPMP inverses

Abstract We generalize the systems of equations, which introduced the MPCEP and *CEPMP inverses, using a minimal rank weak Drazin inverse and a minimal rank right weak Drazin inverse. In order to solve new generalized systems of matrix equations, we define new types of generalized inverses, the so-called weak MPCEP and *CEPMP inverses. The DMP, MPD, MPCEP and *CEPMP inverses are particular kinds of weak MPCEP and *CEPMP inverses. We show characterizations and formulae for weak MPCEP and *CEPMP inverses as well as their perturbation results. As application of weak MPCEP and *CEPMP inverses, we prove solvability of certain linear equations and recover the main application of the Moore–Penrose inverse.