A quantitative version of the converse Taylor theorem: $C^{k,\omega }$-smoothness
Volume 136 / 2014
Colloquium Mathematicum 136 (2014), 57-64
MSC: 46G05, 46T20.
DOI: 10.4064/cm136-1-6
Abstract
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.
