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; added name
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Submitted from: jakub.duda@weizmann.ac.il
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