A Quantitative version of the Converse Taylor theorem: C^k,omega-smoothness

Abstrakt

We prove a uniform version of the converse Taylor theorem in infinite-dimensional spaces with an explicit relation between the moduli of continuity for mappings on a general open domain. We show that if the domain is convex and bounded, then we can extend the estimate up to the boundary.

Klíčová slova

• smoothness
• Taylor's theorem