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Search: All articles in the CJM digital archive with keyword differentiability

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1. CJM Online first

Durand-Cartagena, E.; Ihnatsyeva, L.; Korte, R.; Szumańska, M.
On Whitney-type 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 Whitney-type characterization of approximately differentiable functions in this setting. As an application, we prove a Stepanov-type 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 Radó-Reichelderfer estimate for monotone mappings in finite dimensional spaces that remains valid for DM mappings. This provides an alternative proof of the Fréchet differentiability a.e. of DM mappings. We establish a Morrey-type 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 so-called UDM mappings between Banach spaces, which generalizes the concept of curves of finite variation.

Keywords: monotone mapping, DM mapping, Radó-Reichelderfer property, UDM mapping, differentiability
Categories:26B05, 46G05

3. CJM 2005 (vol 57 pp. 961)

Borwein, Jonathan M.; Wang, Xianfu
Cone-Monotone Functions: Differentiability and Continuity
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
Categories:26B05, 58C20

4. CJM 2004 (vol 56 pp. 825)

Penot, Jean-Paul
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

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