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Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2015, Volume 143, Issue 1, pp. 279 - 288
Let X be a separable Banach space, Y a Banach space and f : X -> Y a mapping. We prove that there exists a sigma-directionally porous set A subset of X such... 
Stepanoff theorem | σ-porous set | Fréchet differentiability | Gâteaux differentiability | σ-directionally porous set | Aronszajn null set | Hadamard differentiability | MATHEMATICS | MATHEMATICS, APPLIED | sigma-porous set | MAPPINGS | Frechet differentiability | Gateaux differentiability | sigma-directionally porous set
Journal Article
Studia Mathematica, ISSN 0039-3223, 2015, Volume 227, Issue 2, pp. 149 - 164
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 07/2019, Volume 292, Issue 7, pp. 1595 - 1626
WDC sets in Rd were recently defined as sublevel sets of DC functions (differences of convex functions) at weakly regular values. They form a natural and... 
WDC set | DC domain | deformation retraction | Gauss–Bonnet formula | Lipschitz manifold | 53C65 | DC aura | 26B25 | DC manifold | MATHEMATICS | CURVATURE MEASURES | Gauss-Bonnet formula
Journal Article
Commentationes Mathematicae Universitatis Carolinae, ISSN 0010-2628, 2016, Volume 57, Issue 1, pp. 21 - 37
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2020, Volume 482, Issue 1, p. 123536
We study closed sets F⊂Rd whose distance function dF≔dist(⋅,F) is DC (i.e., is the difference of two convex functions on Rd). Our main result asserts that if... 
Semiconcave function | DC function | Distance function | Set of positive reach
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 06/2011, Volume 83, Issue 3, pp. 733 - 754
We give a complete characterization of those f: [0, 1] → X (where X is a Banach space that has a Fréchet smooth norm) that allow an equivalent... 
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2015, Volume 423, Issue 1, pp. 594 - 607
Classical Marchaud's theorem (1927) asserts that if f is a bounded function on [a,b], k∈N, and the (k+1)th modulus of smoothness ωk+1(f;t) is so small that... 
Converse Taylor theorem | Marchaud's theorem | [formula omitted]-smoothness | smoothness | MATHEMATICS | MATHEMATICS, APPLIED | C-k,C-w-smoothness | CONVERSE
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2012, Volume 388, Issue 2, pp. 1027 - 1039
We prove a joint generalization of Whitney's C extension theorem and Aversa-Laczkovich-Preiss' extension theorem. It can be roughly described as a theorem on... 
Differentiable functions of several variables | Strict differentiability | Extensions | Whitney's extension theorem | Contingent cone | MATHEMATICS | MATHEMATICS, APPLIED | CLOSED-SETS | DERIVATIVES
Journal Article
Control and Cybernetics, ISSN 0324-8569, 2007, Volume 36, Issue 3, pp. 803 - 810
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 08/2017, Volume 290, Issue 11-12, pp. 1806 - 1829
We give a complete characterization of compact sets with positive reach (proximally C1 sets) in the plane and of one‐dimensional sets with positive reach in... 
52A30 | 26B25 | DC function | Set with positive reach | DC surface | singular point | MATHEMATICS | CURVATURE MEASURES | SINGULARITIES | SPACES | BODIES | CONVEX-FUNCTIONS | CURVES | Mathematics - Metric Geometry
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2015, Volume 143, Issue 1, p. 279
â(or has the Baire property) and is G]]>â 
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2013, Volume 402, Issue 1, pp. 12 - 22
The main known results on differentiability of continuous convex operators f from a Banach space X to an ordered Banach space Y are due to J.M. Borwein and... 
Convex operators | Banach lattices | Fréchet differentiability | Gâteaux differentiability | Ordered normed spaces | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | MAPPINGS | Frechet differentiability | Gateaux differentiability
Journal Article
Journal of Convex Analysis, ISSN 0944-6532, 2013, Volume 20, Issue 2, pp. 573 - 598
Let X be a separable superreflexive Banach space and f be a semiconvex function (with a general modulus) on X. For k epsilon N, let Sigma(k)(f) be the set of... 
Clarke subdifferential | DSC surface | Superreflexive space | Semiconvex function with general modulus | Singular set | Lipschitz surface | Singular point of order K | singular set | superreflexive space | MATHEMATICS | DIFFERENTIABILITY | CONVEX | singular point of order k | LIPSCHITZ FUNCTIONS
Journal Article
Journal of Convex Analysis, ISSN 0944-6532, 2018, Volume 25, Issue 1, pp. 241 - 269
Let f be a continuous real function on a convex subset of a Banach space. We study what can be said about the semiconcavity (with a general modulus) of f, if... 
Semi-Zygmund class | Alpha-midconvex function | Second difference | Jensen semiconcave function | Second modulus of continuity | Semiconcave function with general modulus | MATHEMATICS | alpha-midconvex function | semi-Zygmund class | SEMICONVEX FUNCTIONS | second difference | BANACH-SPACES | second modulus of continuity
Journal Article
05/2019
We study WDC sets, which form a substantial generalization of sets with positive reach and still admit the definition of curvature measures. Main results... 
Mathematics - Classical Analysis and ODEs
Journal Article
04/2019
We study closed sets $F \subset {\mathbb R}^d$ whose distance function $d_F:= {\rm dist}\,(\cdot,F)$ is DC (i.e., is the difference of two convex functions on... 
Mathematics - Classical Analysis and ODEs
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2018, Volume 463, Issue 1, pp. 167 - 175
A problem asked by the authors in 1989 concerns the natural question, whether one can deduce that a continuous function f on an open convex set D⊂Rn is DC... 
d.c. function | DC function | Characterization of DC functions | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Czechoslovak Mathematical Journal, ISSN 0011-4642, 9/2008, Volume 58, Issue 3, pp. 849 - 864
Journal Article
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