Hölder metric regularity of set-valued maps

This paper is devoted to metric regularity of set-valued maps from a complete metric space to a Banach space. In particular we extend a known characterization of the regularity modulus to maps defined on reflexive spaces. The higher order metric regularity, i.e. an extension of metric regularity to Hölder context, is also investigated using high order variations of set-valued maps and results of similar nature are obtained for conical metric regularity.