Implicit Multifunction Theorems In Complete Metric Spaces

Huynh van Ngai (1) , Huu Tron Nguyen (2) , Michel Théra (2)

1 Department of Mathematics, Pedagogical University of Quynhon
2 XLIM-DMI - DMI

In this paper, we establish some new characterizations of metric regularity of implicit multifunctions in complete metric spaces by using lower semicontinuous envelopes of the distance functions to set-valued mappings. Through these new characterizations it is possible to investigate implicit multifunction theorems based on coderivatives and on contingent derivatives as well as the perturbation stability of implicit multifunctions.

Mots clés: Error bound; Perturbation stability; Metric regularity; Implicit multifunction; Generalized equations

Huynh van Ngai, Huu Tron Nguyen, Michel Théra. Implicit Multifunction Theorems In Complete Metric Spaces. Mathematical Programming, 2013, 139 (1-2), pp.301-326. ⟨10.1007/s10107-013-0673-9⟩. ⟨hal-00933872⟩