Narrow Results

Our investigation’s aim is to explore stability and perturbation bounds of positive C₀-semigroups on abstract state spaces by means of the Dobrushin’s ergodicity coefficient. We obtain a linear relation between the stability of the semigroup and the sensitivity of its fixed point with respect to perturbations of C₀-Markov semigroups.

In this paper, perturbation bounds are provided for the $W$-weighted core-EP inverse of a rectangular matrix under reasonable conditions. Perturbation bounds for the core-EP inverse could be stated as a special case. Then, the continuity of the $W$-weighted core-EP inverse is considered from the perspective of equations. Finally, we give an application to a semi-stable matrix involving an integral representation of the $W$-weighted core-EP inverse of a perturbed matrix.