Two stability results of the metric regularity under set-valued perturbation are established. As the perturbation is of addition type, the fi rst result assumes that the graph of the sum mapping is locally closed, the perturbation mapping is locally Lipschitz in the sense of Hausdor metric with the diameter of its image at the reference point being bounded above by a given scalar, while the second result replaces the local closedness of the graph of the sum mapping by both mappings being of closed graph. Compared to a known result, we allow the diameter of the image of the perturbation map- ping at the reference point to vary in a larger area and we apply the Ekeland variational principle only once while the known result using twice. We present an example to which our results can be applied but not the known results.
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Sichuan Normal University, Chengdu, Sichuan, China