  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.
