Perturbation of the weighted core-EP inverse

We obtain two different expressions for the weighted core-EP inverse of the sum A+E for a given operator A and a perturbation operator E, under different conditions on the perturbing operator. As a consequence of these results, we get some relations between idempotents determined by the weighted core-EP inverses of a given operator and its perturbation and we present perturbation bounds for the weighted core-EP inverse. The application to the solution of a perturbed equation is given. We also apply these results to obtain perturbation results for the core-EP inverse.