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Cone-Monotone Functions: Differentiability and Continuity |
Canad. J. Math. 57(2005), 961-982
Published:2005-10-01
Printed: Oct 2005
Printed: Oct 2005
- Jonathan M. Borwein
- Xianfu Wang
Abstract
We provide a porosity-based approach to the differentiability and
continuity of real-valued functions on separable Banach spaces,
when the function is monotone with respect to an ordering induced
by a convex cone $K$ with non-empty interior. We also show that
the set of nowhere $K$-monotone functions has a $\sigma$-porous
complement in the space of continuous functions endowed with the
uniform metric.
| Keywords: | Cone-monotone functions, Aronszajn null set, directionally porous, sets, Gâteaux differentiability, separable space |
| MSC Classifications: |
26B05 - Continuity and differentiation questions 58C20 - Differentiation theory (Gateaux, Frechet, etc.) [See also 26Exx, 46G05] |