Openness Stability and Implicit Multifunction Theorems. Applications to Variational Systems
arXiv:1102.0415 · doi:10.1016/j.na.2011.02.019
Abstract
In this paper we aim to present two general results regarding, on one hand, the openness stability of set-valued maps and, on the other hand, the metric regularity behavior of the implicit multifunction related to a generalized variational system. Then, these results are applied in order to obtain, in a natural way, and in a widely studied case, several relations between the metric regularity moduli of the field maps defining the variational system and the solution map. Our approach allows us to complete and extend several very recent results in literature.
21 pages
References in corpus (1)
Cited by in corpus (6)
- On semiregularity of mappings
- On Parametric Vector Optimization via Metric Regularity of Constraint Systems
- On Differential Properties of Multifunctions Defined Implicitly by Set-Valued Inclusions
- Filling the Gap between Metric Regularity and Fixed Points: The Linear Openness of Compositions
- Metric regularity of composition set-valued mappings: metric setting and coderivative conditions
- On Subregularity Properties of Set-Valued Mappings. Applications to Solid Vector Optimization