Lyusternik-Graves Theorem for Holder Metric Regularity

The paper extends the well-known Lyusternik-Graves theorem for set-valued mappings to the Holder framework, offers an affirmative answer to an open problem proposed by Dontchev and improves recent results of He and Ng. Primal and dual necessary and sufficient conditions for Holder metric regularity are established. The results are applied to convergence analysis of a Newton-type method. Some open problems for future research are also discussed.