## Lyusternik-Graves Theorems for the Sum of a Lipschitz Function and a Set-valued Mapping

- Radek Cibulka, Asen L. Dontchev, Vladimir M. Veliov
- SIAM J. Control and Optimization
- 2016

@article{Cibulka2013ANO, title={A note on Robinson-Ursescu and Lyusternik-Graves theorem}, author={Radek Cibulka and Mari{\'a}n Fabian}, journal={Math. Program.}, year={2013}, volume={139}, pages={89-101} }

- Published 2013 in Math. Program.
DOI:10.1007/s10107-013-0662-z

The aim of this note is twofold. First, we prove an analogue of the wellknown Robinson–Ursescu Theorem on the relative openness with a linear rate (restrictive metric regularity) of a multivalued mapping. Second, we prove a generalization of Graves Open Mapping Theorem for a class of mappings which can be approximated at a reference point by a bunch of linear mappings. The approximated non-linear mapping is restricted to a closed convex subset of a Banach space.