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

M. Bianchi (), G. Kassay () and R. Pini ()
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M. Bianchi: Università Cattolica del Sacro Cuore
G. Kassay: Babeş-Bolyai University
R. Pini: Università degli Studi di Milano-Bicocca

Journal of Optimization Theory and Applications, 2015, vol. 164, issue 1, No 4, 92-108

Abstract: Abstract In this paper, we present the notions of openness and metric regularity for a set-valued map with respect to two fixed sets, proving their equivalence. By using different approaches, we show the stability, with respect to the sum of maps, of the 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.

Keywords: Linear openness; Metric regularity; Sum of maps; Generalized equation; Sensitivity analysis; Fixed point theorem; Ekeland’s variational principle; 49J53; 49K40; 90C31 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10957-014-0560-4

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