Slopes of Multifunctions and Extensions of Metric Regularity

Huynh van Ngai (1) , Alexander Kruger , Michel Théra (2)

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

This article aims to demonstrate how the definitions of slopes can be extended to multi-valued mappings between metric spaces and applied for characterizing metric regularity. Several kinds of local and nonlocal slopes are defined and several metric regularity properties for set-valued mappings between metric spaces are investigated.

Mots clés: Variational analysis; error bounds; slope; multifunction; metric regularity

Huynh van Ngai, Alexander Kruger, Michel Théra. Slopes of Multifunctions and Extensions of Metric Regularity. Vietnam Journal of Mathematics, 2012, 40 (2-3), pp.355-369. ⟨hal-00934927⟩