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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
Letters in Mathematical Physics, ISSN 0377-9017, 02/2018, Volume 108, Issue 2, pp. 285 - 306
.... For certain admissible perturbations of the pair potential and sufficiently small activity, we rigorously establish Frechet differentiability with respect to the supremum norm in the image space... 
Kirkwood–Salsburg equations | Statistical mechanics | Fréchet derivative | Molecular distribution function | Analysis | Distribution (Probability theory)
Journal Article
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, ISSN 1417-3875, 2019, Volume 2019, Issue 13, pp. 1 - 44
In infinite-dimensional spaces there are non-equivalent notions of continuous differentiability which can be used to derive the familiar results of calculus up to the Implicit Function Theorem and beyond... 
MATHEMATICS | MATHEMATICS, APPLIED | unbounded delay | C-1-SMOOTHNESS | Frechet space | semiflow | invariant manifolds | Frechet differentiability | delay differential equation | MANIFOLD | frechet differentiability | fréchet space
Journal Article
Advances in Mathematics, ISSN 0001-8708, 09/2014, Volume 262, pp. 436 - 475
One of the long standing questions in the theory of Schatten–von Neumann ideals of compact operators is whether their norms have the same differentiability properties as the norms of their commutative counterparts... 
Fréchet differentiability | Schatten p-norms | Multiple operator integrals
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 2/2018, Volume 108, Issue 2, pp. 307 - 329
.... For certain admissible perturbations of the pair potential and sufficiently small activity we rigorously establish Frechet differentiability of the Ursell function in the $$L^1$$ L 1 norm... 
Fréchet derivative | Theoretical, Mathematical and Computational Physics | Complex Systems | Cluster expansion | 82B21 | 82B80 | Ursell function | Physics | Molecular distribution function | Geometry | Radial distribution function | Group Theory and Generalizations | Statistical mechanics | Analysis | Distribution (Probability theory)
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 N.K. Kirov... 
Convex operators | Banach lattices | Fréchet differentiability | Gâteaux differentiability | Ordered normed spaces | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | MAPPINGS | Frechet differentiability | Gateaux differentiability
Journal Article
2012, 1, Annals of mathematics studies, ISBN 9780691153551, Volume no. 179, ix, 425
This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into... 
Calculus of variations | Functional analysis | Banach spaces | Mathematics | Math | Frechet spaces | Lipschitz spaces
Book
Inventiones Mathematicae, ISSN 0020-9910, 2014, Volume 199, Issue 2, pp. 517 - 559
We show that if then there exists a Lebesgue null set in containing a point of differentiability of each Lipschitz function... 
HAUSDORFF DIMENSION | MATHEMATICS | FRECHET DIFFERENTIABILITY | Functions (mathematics) | Texts | Theorems | Mathematical analysis | Avoidance | Proving
Journal Article
Acta Mathematica Hungarica, ISSN 0236-5294, 2/2015, Volume 145, Issue 1, pp. 174 - 190
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2016, Volume 434, Issue 1, pp. 182 - 190
In this paper, author proves that if X1 and X2 are Gâteaux differentiable space, then X1 and X2 have the ball-covering property if and only if (X1×X2,‖⋅‖p) and... 
Gâteaux differentiable space | Ball-covering property | Convex function | MATHEMATICS | MATHEMATICS, APPLIED | MAPPINGS | WEAK ASPLUND SPACES | Gateaux differentiable space | CONVEX-FUNCTIONS | FRECHET DIFFERENTIABILITY | Bisphenol-A
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 360, Issue 2, pp. 503 - 517
.... Then the solution map is shown to be weakly Gâteux differentiable on P, implying the Gâteux differentiability of the objective function... 
Fréchet differentiability | Parameter identification | Optimal control | MATHEMATICS | MATHEMATICS, APPLIED | Frechet differentiability | PARAMETERS | IDENTIFICATION
Journal Article
Optimization, ISSN 0233-1934, 02/2015, Volume 64, Issue 2, pp. 365 - 388
Journal Article
Journal of Inverse and Ill-posed Problems, ISSN 0928-0219, 04/2018, Volume 26, Issue 2, pp. 211 - 227
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 2/2018, Volume 108, Issue 2, pp. 285 - 306
... activity, we rigorously establish Frechet differentiability with respect to the supremum norm in the image space... 
Geometry | Kirkwood–Salsburg equations | Fréchet derivative | Theoretical, Mathematical and Computational Physics | Complex Systems | Group Theory and Generalizations | 82B21 | Statistical mechanics | 82B80 | Physics | Molecular distribution function
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2011, Volume 261, Issue 6, pp. 1674 - 1710
We show that any non-zero Banach space with a separable dual contains a totally disconnected, closed and bounded subset S of Hausdorff dimension 1 such that... 
Fréchet differentiability | Universal differentiability set | Null set | MATHEMATICS | LIPSCHITZ FUNCTIONS | Frechet differentiability | POINTS
Journal Article
Israel Journal of Mathematics, ISSN 0021-2172, 10/2012, Volume 191, Issue 2, pp. 889 - 900
We give a short proof that any non-zero Euclidean space has a compact subset of Hausdorff dimension one that contains a differentiability point of every real... 
Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | LIPSCHITZ FUNCTIONS | FRECHET DIFFERENTIABILITY | BANACH-SPACES
Journal Article
The Annals of Statistics, ISSN 0090-5364, 4/2009, Volume 37, Issue 2, pp. 939 - 960
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 346, Issue 2, pp. 374 - 383
In this paper we establish the strong Fréchet differentiability of maps from the set of initial values and forcing terms into the set of solutions for semilinear second order evolution equations... 
Second order evolution equations | Semilinear damped wave equations | Fréchet differentiability | Gâteaux differentiability | MATHEMATICS | MATHEMATICS, APPLIED | second order evolution equations | Frechet differentiability | semilinear damped wave equations | Gateaux differentiability
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2020, Volume 489, Issue 2, p. 124171
... points of Gâteaux differentiability of the norm. In particular, we show that Gâteaux and Fréchet differentiability are equivalent for finitely supported elements of Lipschitz... 
Fréchet differentiability | Gâteaux differentiability | Lipschitz-free space | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | Frechet differentiability | OCTAHEDRALITY | Gateaux differentiability
Journal Article
Positivity, ISSN 1385-1292, 9/2011, Volume 15, Issue 3, pp. 527 - 536
Journal Article
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