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

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)

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

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

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)

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

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

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

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

... (for vector functions) can be inferred from the corresponding theorem of Radamacher type. Finally we present Stepanov type differentiability theorems with the assumption...

{\Gamma}$$ Γ -nullset | Fréchet differentiability | Gâteaux differentiability | primary 46G05 | secondary 46T20 | pointwise Lipschitz function | Rademacher’s theorem | Mathematics, general | Mathematics | metric differentiability | Stepanov’s theorem | w differentiability | Γ-nullset | wdifferentiability | Gamma-null set | METRIC-SPACES | Rademacher's theorem | Gateaux differentiability | MATHEMATICS | Stepanov's theorem | POINTWISE LIPSCHITZ MAPPINGS | w-differentiability | MAPS | BANACH-SPACES | Frechet differentiability

{\Gamma}$$ Γ -nullset | Fréchet differentiability | Gâteaux differentiability | primary 46G05 | secondary 46T20 | pointwise Lipschitz function | Rademacher’s theorem | Mathematics, general | Mathematics | metric differentiability | Stepanov’s theorem | w differentiability | Γ-nullset | wdifferentiability | Gamma-null set | METRIC-SPACES | Rademacher's theorem | Gateaux differentiability | MATHEMATICS | Stepanov's theorem | POINTWISE LIPSCHITZ MAPPINGS | w-differentiability | MAPS | BANACH-SPACES | Frechet differentiability

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

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

Fréchet differentiability | Parameter identification | Optimal control | MATHEMATICS | MATHEMATICS, APPLIED | Frechet differentiability | PARAMETERS | IDENTIFICATION

Journal Article

12.
Full Text
On differentiability properties of player convex generalized Nash equilibrium problems

Optimization, ISSN 0233-1934, 02/2015, Volume 64, Issue 2, pp. 365 - 388

This article studies differentiability properties for a reformulation of a player convex generalized Nash equilibrium problem as a constrained and possibly nonsmooth minimization problem...

Nikaido-Isoda function | Gâteaux differentiability | Fréchet differentiability | generalized Nash equilibrium problem | player convexity | parametric optimization | Nikaido–Isoda function | MATHEMATICS, APPLIED | RELAXATION ALGORITHMS | MULTIPLIERS | Gateaux differentiability | 90C31 | 91A10 | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPTIMIZATION | Frechet differentiability | Minimization | Mathematical models | Constraints | Mathematical analysis | Optimization | Players

Nikaido-Isoda function | Gâteaux differentiability | Fréchet differentiability | generalized Nash equilibrium problem | player convexity | parametric optimization | Nikaido–Isoda function | MATHEMATICS, APPLIED | RELAXATION ALGORITHMS | MULTIPLIERS | Gateaux differentiability | 90C31 | 91A10 | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPTIMIZATION | Frechet differentiability | Minimization | Mathematical models | Constraints | Mathematical analysis | Optimization | Players

Journal Article

Journal of Inverse and Ill-posed Problems, ISSN 0928-0219, 04/2018, Volume 26, Issue 2, pp. 211 - 227

.... We prove the Frechet differentiability in Besov spaces, and derive the formula for the Frechet differential under minimal regularity assumptions on the data...

35K20 | embedding theorems | 35R30 | parabolic free boundary problem | Inverse Stefan problem | optimal control of parabolic PDE | 35R35 | Frechet differentiability | trace embeddings | Besov spaces | MATHEMATICS, APPLIED | APPROXIMATION | CAUCHY-PROBLEM | MATHEMATICS | HEAT-EQUATION | CONVERGENCE | Boundary value problems | Research | Banach spaces | Mathematical research | Function space | Optimal control | Free boundaries | Heat transfer | Heat flux | Mathematics - Analysis of PDEs

35K20 | embedding theorems | 35R30 | parabolic free boundary problem | Inverse Stefan problem | optimal control of parabolic PDE | 35R35 | Frechet differentiability | trace embeddings | Besov spaces | MATHEMATICS, APPLIED | APPROXIMATION | CAUCHY-PROBLEM | MATHEMATICS | HEAT-EQUATION | CONVERGENCE | Boundary value problems | Research | Banach spaces | Mathematical research | Function space | Optimal control | Free boundaries | Heat transfer | Heat flux | Mathematics - Analysis of PDEs

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

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

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

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

The paper aims at finding widely and smoothly defined nonparametric location and scatter functionals. As a convenient vehicle, maximum likelihood estimation of...

Critical points | Linear transformations | Maximum likelihood estimators | Polynomials | Mathematical functions | Matrices | Mathematics | Vector spaces | Banach space | Implicit functions | Weakly continuous | Affinely equivariant | Fréchet differentiable | EM ALGORITHM | DESCRIPTIVE STATISTICS | CAUCHY DISTRIBUTION | DONSKER CLASSES | STATISTICS & PROBABILITY | MULTIVARIATE LOCATION | UNIMODALITY | weakly continuous | Frechet differentiable | NONPARAMETRIC MODELS | LIKELIHOOD | 62G05 | 62GH20 | 62G35

Critical points | Linear transformations | Maximum likelihood estimators | Polynomials | Mathematical functions | Matrices | Mathematics | Vector spaces | Banach space | Implicit functions | Weakly continuous | Affinely equivariant | Fréchet differentiable | EM ALGORITHM | DESCRIPTIVE STATISTICS | CAUCHY DISTRIBUTION | DONSKER CLASSES | STATISTICS & PROBABILITY | MULTIVARIATE LOCATION | UNIMODALITY | weakly continuous | Frechet differentiable | NONPARAMETRIC MODELS | LIKELIHOOD | 62G05 | 62GH20 | 62G35

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

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

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

This paper revisits the duality between differentiability and strict or strong convexity under the Legendre–Fenchel transform $${f\mapsto f...

Essential Gâteaux differentiability | Essential strict convexity | Mathematics | Essential strong convexity | Operator Theory | Fourier Analysis | Potential Theory | Calculus of Variations and Optimal Control; Optimization | Legendre–Fenchel transform | Essential Fréchet differentiability | 49J50 | Econometrics | 46G05 | 46N10 | Legendre-Fenchel transform | Studies | Theorems | Banach spaces

Essential Gâteaux differentiability | Essential strict convexity | Mathematics | Essential strong convexity | Operator Theory | Fourier Analysis | Potential Theory | Calculus of Variations and Optimal Control; Optimization | Legendre–Fenchel transform | Essential Fréchet differentiability | 49J50 | Econometrics | 46G05 | 46N10 | Legendre-Fenchel transform | Studies | Theorems | Banach spaces

Journal Article

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