On Gateaux differentiability of pointwise Lipschitz mappings
| dc.creator | Duda, Jakub | |
| dc.date | 2005-11-22 | |
| dc.date | 2006-07-30 | |
| dc.date.accessioned | 2026-07-07T06:51:37Z | |
| dc.date.available | 2026-07-07T06:51:37Z | |
| dc.description | We prove that for every function $f:X\to Y$, where $X$ is a separable Banach space and $Y$ is a Banach space with RNP, there exists a set $A\in\tilde\mcA$ such that $f$ is Gateaux differentiable at all $x\in S(f)\setminus A$, where $S(f)$ is the set of points where $f$ is pointwise-Lipschitz. This improves a result of Bongiorno. As a corollary, we obtain that every $K$-monotone function on a separable Banach space is Hadamard differentiable outside of a set belonging to $\tilde\mcC$; this improves a result due to Borwein and Wang. Another corollary is that if $X$ is Asplund, $f:X\to\R$ cone monotone, $g:X\to\R$ continuous convex, then there exists a point in $X$, where $f$ is Hadamard differentiable and $g$ is Frechet differentiable. | |
| dc.description | 11 pages; updated version | |
| dc.identifier | https://arxiv.org/abs/math/0511565 | |
| dc.identifier | http://arxiv.org/abs/math/0511565 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/105046 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46G05; 46T20 | |
| dc.title | On Gateaux differentiability of pointwise Lipschitz mappings | |
| dc.type | text |