1. CJM 2013 (vol 66 pp. 721)
 DurandCartagena, E.; Ihnatsyeva, L.; Korte, R.; Szumańska, M.

On Whitneytype Characterization of Approximate Differentiability on Metric Measure Spaces
We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitneytype characterization of approximately differentiable functions in this setting.
As an application, we prove a Stepanovtype theorem and consider approximate differentiability of Sobolev, $BV$ and maximal functions.
Keywords:approximate differentiability, metric space, strong measurable differentiable structure, Whitney theorem Categories:26B05, 28A15, 28A75, 46E35 

2. CJM 2011 (vol 63 pp. 460)
 Pavlíček, Libor

Monotonically Controlled Mappings
We study classes of mappings between finite and infinite dimensional
Banach spaces that are monotone and mappings which are differences
of monotone mappings (DM). We prove a RadÃ³Reichelderfer estimate
for monotone mappings in finite dimensional spaces that remains
valid for DM mappings. This provides an alternative proof of the
FrÃ©chet differentiability a.e. of DM mappings. We establish a
Morreytype estimate for the distributional derivative of monotone
mappings. We prove that a locally DM mapping between finite
dimensional spaces is also globally DM. We introduce and study a new
class of the socalled UDM mappings between Banach spaces, which
generalizes the concept of curves of finite variation.
Keywords: monotone mapping, DM mapping, RadÃ³Reichelderfer property, UDM mapping, differentiability Categories:26B05, 46G05 

3. CJM 2005 (vol 57 pp. 961)
 Borwein, Jonathan M.; Wang, Xianfu

ConeMonotone Functions: Differentiability and Continuity
We provide a porositybased approach to the differentiability and
continuity of realvalued functions on separable Banach spaces,
when the function is monotone with respect to an ordering induced
by a convex cone $K$ with nonempty 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:Conemonotone functions, Aronszajn null set, directionally porous, sets, GÃ¢teaux differentiability, separable space Categories:26B05, 58C20 

4. CJM 2004 (vol 56 pp. 699)
 Gaspari, Thierry

Bump Functions with HÃ¶lder Derivatives
We study the range of the gradients
of a $C^{1,\al}$smooth bump function defined on a Banach space.
We find that this set must satisfy two geometrical conditions:
It can not be too flat and it satisfies a strong compactness condition
with respect to an appropriate distance.
These notions are defined precisely below.
With these results we illustrate the differences with
the case of $C^1$smooth bump functions.
Finally, we give a sufficient condition on a subset of $X^{\ast}$ so that it is
the set of the gradients of a $C^{1,1}$smooth bump function.
In particular, if $X$ is an infinite dimensional Banach space
with a $C^{1,1}$smooth bump function,
then any convex open bounded subset of $X^{\ast}$ containing $0$ is the set
of the gradients of a $C^{1,1}$smooth bump function.
Keywords:Banach space, bump function, range of the derivative Categories:46T20, 26E15, 26B05 

5. CJM 2004 (vol 56 pp. 825)
 Penot, JeanPaul

Differentiability Properties of Optimal Value Functions
Differentiability properties of optimal value functions associated with
perturbed optimization problems require strong assumptions. We consider such
a set of assumptions which does not use compactness hypothesis but which
involves a kind of coherence property. Moreover, a strict differentiability
property is obtained by using techniques of Ekeland and Lebourg and a result
of Preiss. Such a strengthening is required in order to obtain genericity
results.
Keywords:differentiability, generic, marginal, performance function, subdifferential Categories:26B05, 65K10, 54C60, 90C26, 90C48 
