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

Lyusternik-Graves Theorem for Holder Metric Regularity