Perturbation formulae for the generalized core–EP inverse

The aim of this paper is to present perturbation formulae and perturbation bounds for the GCEP inverse, gMP inverse and their duals. We also study equivalent conditions for absorption laws of the GCEP inverse, the gMP inverse and their duals and use these results to get perturbation bounds. Applying the GCEP and *GCEP inverses, we introduce two new binary relations and show that they are partial orders on corresponding set.