In this paper we present the notions of (U; V )-openness and (U; V )- metric regularity for a set-valued map, proving their equivalence. By using different approaches we show the stability, with respect to the sum of maps, of the (U; V )-openness property, both in the setting of Banach spaces, and of metric spaces. Finally, we infer the regularity of the map solving a generalized parametric equation defined via a parametric map that is, in its turn, perturbed by the sum with another map.

Kassay, G., Bianchi, M., Pini, R., Stability Results of Variational Systems Under Openness with Respect to Fixed Sets, <<JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS>>, 2015; (164): 92-108. [doi:10.1007/s10957-014-0560-4] [http://hdl.handle.net/10807/55439]

Stability Results of Variational Systems Under Openness with Respect to Fixed Sets

Bianchi, Monica;
2015

Abstract

In this paper we present the notions of (U; V )-openness and (U; V )- metric regularity for a set-valued map, proving their equivalence. By using different approaches we show the stability, with respect to the sum of maps, of the (U; V )-openness property, both in the setting of Banach spaces, and of metric spaces. Finally, we infer the regularity of the map solving a generalized parametric equation defined via a parametric map that is, in its turn, perturbed by the sum with another map.
2015
Inglese
Kassay, G., Bianchi, M., Pini, R., Stability Results of Variational Systems Under Openness with Respect to Fixed Sets, <<JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS>>, 2015; (164): 92-108. [doi:10.1007/s10957-014-0560-4] [http://hdl.handle.net/10807/55439]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/55439
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