# [Banach] Abstract of a paper by Jakub Duda

Dale Alspach alspach at www.math.okstate.edu
Wed Aug 2 16:58:08 CDT 2006

This is an announcement for the paper "On Gateaux differentiability
of pointwise Lipschitz mappings" by Jakub Duda.

Abstract: 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.

Archive classification: Functional Analysis

Mathematics Subject Classification: 46G05; 46T20

Remarks: 11 pages; updated version

The source file(s), ongatdif.tex: 43273 bytes, is(are) stored in
gzipped form as 0511565.gz with size 13kb. The corresponding postcript
file has gzipped size 61kb.

Submitted from: jakub.duda at weizmann.ac.il

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http://front.math.ucdavis.edu/math.FA/0511565

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http://arXiv.org/abs/math.FA/0511565

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