TY - JOUR
T1 - Stability Results of Variational Systems Under Openness with Respect to Fixed Sets
AU - Kassay, G.
AU - Bianchi, Monica
AU - Pini, R.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
KW - Generalized equation
KW - Linear openness
KW - Sum of maps
KW - Generalized equation
KW - Linear openness
KW - Sum of maps
UR - http://hdl.handle.net/10807/55439
U2 - 10.1007/s10957-014-0560-4
DO - 10.1007/s10957-014-0560-4
M3 - Article
SN - 0022-3239
SP - 92
EP - 108
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
ER -