Banach Space Theory: Regularity Criteria

Abstract

This chapter opens the study of local regularity theory for mappings between Banach (and more generally, normed) spaces – the primary interest of variational analysis in general and regularity theory in particular. Tangent and subdifferential constructions offer a convenient and efficient instrument for the study of regularity phenomena in Banach spaces. True, as we have already mentioned, the criteria based on such constructions may be less precise than the metric criteria studied in the second and third chapters. But they do provide estimates which are often sufficient for applications and may be computationally more tractable, especially when dealing with objects specific to Banach spaces.