ESAIM - Probability and Statistics, ISSN 1292-8100, 2018, Volume 22, pp. 19 - 34

We develop a family of infinite-dimensional (non-parametric) manifolds of probability measures. The latter are defined on underlying Banach spaces, and have...

Information geometry | Fisher-Rao Metric | Fréchet manifold | Banach manifold | Non-parametric statistics | SPACE | information geometry | non-parametric statistics | STATISTICS & PROBABILITY | EXPONENTIAL STATISTICAL MANIFOLD | Frechet manifold | GEOMETRY | Statistical analysis | Derivatives | Banach space | Manifolds (mathematics) | Continuity (mathematics)

Information geometry | Fisher-Rao Metric | Fréchet manifold | Banach manifold | Non-parametric statistics | SPACE | information geometry | non-parametric statistics | STATISTICS & PROBABILITY | EXPONENTIAL STATISTICAL MANIFOLD | Frechet manifold | GEOMETRY | Statistical analysis | Derivatives | Banach space | Manifolds (mathematics) | Continuity (mathematics)

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2008, Volume 69, Issue 4, pp. 1112 - 1124

We continue the study of the calculus of the generalized subdifferentials started in [V.F. Demyanov, V. Roshchina, Exhausters and subdifferentials in nonsmooth...

Calculus of subdifferentials | Upper exhausters | Fréchet subdifferential | upper exhausters | MATHEMATICS | Frechet subdifferential | MATHEMATICS, APPLIED | calculus of subdifferentials

Calculus of subdifferentials | Upper exhausters | Fréchet subdifferential | upper exhausters | MATHEMATICS | Frechet subdifferential | MATHEMATICS, APPLIED | calculus of subdifferentials

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2009, Volume 137, Issue 5, pp. 1743 - 1752

Results on factorization (through linear operators) of polynomials and holomorphic mappings between Banach spaces have been obtained in recent years by several...

Mean value theorems | Mathematical theorems | Polynomials | Banach space | Factorization | Cilia | Perceptron convergence procedure | Compact operator | Weakly continuous function | Fréchet differentiable mapping | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | BANACH-SPACES | weakly continuous function | Frechet differentiable mapping | HOLOMORPHIC MAPPINGS | factorization | compact operator

Mean value theorems | Mathematical theorems | Polynomials | Banach space | Factorization | Cilia | Perceptron convergence procedure | Compact operator | Weakly continuous function | Fréchet differentiable mapping | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | BANACH-SPACES | weakly continuous function | Frechet differentiable mapping | HOLOMORPHIC MAPPINGS | factorization | compact operator

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 12/2016, Volume 10, Issue 8, pp. 1695 - 1703

In this paper, we shall offer two inequalities for differentiable mappings which the induced maps by them on the set of Hermitian operators are operator...

Operator Theory | 46G10 | Fréchet differentiable functions | Operator inequalities | Analysis | Mathematics, general | Mathematics | Hermite–Hadamard inequality | 46G05 | 47A63 | MATHEMATICS | MATHEMATICS, APPLIED | Hermite-Hadamard inequality | Frechet differentiable functions

Operator Theory | 46G10 | Fréchet differentiable functions | Operator inequalities | Analysis | Mathematics, general | Mathematics | Hermite–Hadamard inequality | 46G05 | 47A63 | MATHEMATICS | MATHEMATICS, APPLIED | Hermite-Hadamard inequality | Frechet differentiable functions

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

Advances in Pure and Applied Mathematics, ISSN 1867-1152, 07/2018, Volume 9, Issue 3, pp. 167 - 184

In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is...

convex minimization problem | Legendre functions | Gâteaux differentiable function | Bregman distance | strong convergence | Bregman projection | Fréchet differentiable functions | 47H09 | variational inequality, reflexive Banach space | 47J05 | 47J25 | resolvent | 47H06 | reffexive Banach space | variational inequality | Iterative algorithms | Error analysis | Banach spaces | Banach space | Optimization

convex minimization problem | Legendre functions | Gâteaux differentiable function | Bregman distance | strong convergence | Bregman projection | Fréchet differentiable functions | 47H09 | variational inequality, reflexive Banach space | 47J05 | 47J25 | resolvent | 47H06 | reffexive Banach space | variational inequality | Iterative algorithms | Error analysis | Banach spaces | Banach space | Optimization

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 9/2008, Volume 12, Issue 6, pp. 1477 - 1492

We prove that an approximately convex function on an open subset of an Asplund space is generically Fréchet differentiable, as are genuine convex functions....

Mathematical theorems | Decreasing sequences | Mathematical functions | Convexity | Vector spaces | Banach space | Continuous functions | Approximately convex function | Differentiability | Asplund space | Genericity | Fréchet derivative | MATHEMATICS | MONOTONE | differentiability | genericity | BANACH-SPACES | Frechet derivative | MEAN-VALUE THEOREM | approximately convex function | ALPHA(CENTER-DOT)-MONOTONE MULTIFUNCTIONS

Mathematical theorems | Decreasing sequences | Mathematical functions | Convexity | Vector spaces | Banach space | Continuous functions | Approximately convex function | Differentiability | Asplund space | Genericity | Fréchet derivative | MATHEMATICS | MONOTONE | differentiability | genericity | BANACH-SPACES | Frechet derivative | MEAN-VALUE THEOREM | approximately convex function | ALPHA(CENTER-DOT)-MONOTONE MULTIFUNCTIONS

Journal Article

Filomat, ISSN 0354-5180, 1/2017, Volume 31, Issue 11, pp. 3407 - 3420

Some necessary conditions for having nonempty weak subdifferential of a function are presented and the positively homogeneous of the weak subdifferential...

Mathematical functions | Fréchet differentiable function | Locally Lipchitz function | Weak subgradient | Weak subdifferential | weak subgradient | MATHEMATICS | MATHEMATICS, APPLIED | Frechet differentiable function | OPTIMIZATION | weak subdifferential | locally Lipchitz function | RADIAL EPIDERIVATIVES

Mathematical functions | Fréchet differentiable function | Locally Lipchitz function | Weak subgradient | Weak subdifferential | weak subgradient | MATHEMATICS | MATHEMATICS, APPLIED | Frechet differentiable function | OPTIMIZATION | weak subdifferential | locally Lipchitz function | RADIAL EPIDERIVATIVES

Journal Article

Publications of the Research Institute for Mathematical Sciences, ISSN 0034-5318, 2000, Volume 36, Issue 1, pp. 139 - 157

We study the Banach *-algebra C1QP(I) of C1-functions on the compact interval I such that the corresponding Hilbert space operator function T → f(T), for T =...

General | Functional analysis | Operator theory | commutator equations | C∗-algebra | operator differentiability | Fréchet derivative

General | Functional analysis | Operator theory | commutator equations | C∗-algebra | operator differentiability | Fréchet derivative

Journal Article

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, ISSN 0895-4798, 2019, Volume 40, Issue 2, pp. 774 - 799

We study the structured condition number of differentiable maps between smooth matrix manifolds, extending previous results to maps that are only...

structured matrices | MATHEMATICS, APPLIED | structured condition number | Frechet derivative | DECOMPOSITION | polar decomposition | Jordan algebra | bilinear form | matrix function | automorphism group | sesquilinear form | Lie algebra | condition number

structured matrices | MATHEMATICS, APPLIED | structured condition number | Frechet derivative | DECOMPOSITION | polar decomposition | Jordan algebra | bilinear form | matrix function | automorphism group | sesquilinear form | Lie algebra | condition number

Journal Article

Demonstratio Mathematica, ISSN 0420-1213, 08/2017, Volume 50, Issue 1, pp. 208 - 222

Here we study quantitatively the high degree of approximation of sequences of linear operators acting on Banach space valued Fréchet differentiable functions...

41A25 | 41A36 | Continuous Banach space valued functions | rate of convergence | modulus of continuity | positive linear operator | Banach space valued Fréchet differentiable functions | convexity | 41A17 | Convexity | Positive linear operator | Continuous banach space valued functions | Rate of convergence | Modulus of continuity | Banach space valued Fréchet dierentiable functions

41A25 | 41A36 | Continuous Banach space valued functions | rate of convergence | modulus of continuity | positive linear operator | Banach space valued Fréchet differentiable functions | convexity | 41A17 | Convexity | Positive linear operator | Continuous banach space valued functions | Rate of convergence | Modulus of continuity | Banach space valued Fréchet dierentiable functions

Journal Article

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, ISSN 1310-1331, 2019, Volume 72, Issue 2, pp. 152 - 157

We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.

Nash-Moser-Ekeland theory | surjectivity | Frechet space | Gateaux differentiable function | MULTIDISCIPLINARY SCIENCES

Nash-Moser-Ekeland theory | surjectivity | Frechet space | Gateaux differentiable function | MULTIDISCIPLINARY SCIENCES

Journal Article

13.
BERNSTEIN FUNCTIONS OF SEVERAL SEMIGROUP GENERATORS ON BANACH SPACES UNDER BOUNDED PERTURBATIONS, II

OPERATORS AND MATRICES, ISSN 1846-3886, 06/2018, Volume 12, Issue 2, pp. 445 - 463

The paper deals with multidimensional Bochner-Phillips functional calculus. In the previous paper by the author bounded perturbations of Bernstein functions of...

MATHEMATICS | Bochner-Phillips functional calculus | Bernstein function | perturbation of an operator | spectral shift function | Livschits-Krein trace formula | perturbation determinant | TRACE FORMULA | OPERATORS | Frechet-differentiable function | semigroup of operators

MATHEMATICS | Bochner-Phillips functional calculus | Bernstein function | perturbation of an operator | spectral shift function | Livschits-Krein trace formula | perturbation determinant | TRACE FORMULA | OPERATORS | Frechet-differentiable function | semigroup of operators

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 12/2019, Volume 267, Issue 12, pp. 7263 - 7312

We prove that a general class of nonlinear, non-autonomous odes in Fréchet spaces are close to odes in a specific normal form, where closeness means that...

Differentiable and polynomial maps between Fréchet spaces | Nonlinear | Invariant manifold | Non-autonomous pde | Normal form | MATHEMATICS | Differentiable and polynomial maps between Frechet spaces | APPROXIMATION | Non-autonomous PDE

Differentiable and polynomial maps between Fréchet spaces | Nonlinear | Invariant manifold | Non-autonomous pde | Normal form | MATHEMATICS | Differentiable and polynomial maps between Frechet spaces | APPROXIMATION | Non-autonomous PDE

Journal Article

Annales de l'Institut Fourier, ISSN 0373-0956, 2014, Volume 64, Issue 1, pp. 297 - 325

We exhibit the first examples of Frechet spaces which contain a closed infinite dimensional subspace of universal series, but no restricted universal series....

Taylor series | Universal series | Infinitely differentiable real functions | Universality | Spaceability | universality | MATHEMATICS | infinitely differentiable real functions | HYPERCYCLIC SUBSPACES | SERIES | THEOREM | FRECHET SPACE | spaceability | universal series | OPERATORS

Taylor series | Universal series | Infinitely differentiable real functions | Universality | Spaceability | universality | MATHEMATICS | infinitely differentiable real functions | HYPERCYCLIC SUBSPACES | SERIES | THEOREM | FRECHET SPACE | spaceability | universal series | OPERATORS

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

Optimization Letters, ISSN 1862-4472, 12/2014, Volume 8, Issue 8, pp. 2227 - 2243

In this paper, we first prove a lemma about the lower semicontinuity of the distance function in infinite dimensional spaces, which is crucial to openness...

Openness | Computational Intelligence | Fréchet subdifferential | Operations Research/Decision Theory | Fréchet coderivative | Proximinal set | Numerical and Computational Physics | Mathematics | Fréchet differentiable | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MULTIFUNCTIONS | REGULARITY | STABILITY | Frechet subdifferential | Frechet coderivative | Frechet differentiable | IMPLICIT FUNCTION THEOREMS

Openness | Computational Intelligence | Fréchet subdifferential | Operations Research/Decision Theory | Fréchet coderivative | Proximinal set | Numerical and Computational Physics | Mathematics | Fréchet differentiable | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MULTIFUNCTIONS | REGULARITY | STABILITY | Frechet subdifferential | Frechet coderivative | Frechet differentiable | IMPLICIT FUNCTION THEOREMS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2001, Volume 253, Issue 1, pp. 290 - 296

A convex Fréchet differentiable function is minimized subject to a certain hyperplane at a point if the function is minimized in all directions which are...

convex function | quadratic programming | Fréchet differentiable | Fré | chet differentiable | Convex function; Fréchet differentiable; quadratic programming | MATHEMATICS | MATHEMATICS, APPLIED | Frechet differentiable

convex function | quadratic programming | Fréchet differentiable | Fré | chet differentiable | Convex function; Fréchet differentiable; quadratic programming | MATHEMATICS | MATHEMATICS, APPLIED | Frechet differentiable

Journal Article

Mathematical Notes, ISSN 0001-4346, 2/2012, Volume 91, Issue 1, pp. 153 - 160

We construct here an example of a continuous convex function on a locally convex space, which is MS-differentiable at a point, but is not HL-differentiable at...

Fréchet differentiability | topological vector space | Mathematics, general | convex function | MS- differentiability | Mathematics | Minkowski function | balanced absorbing subset | HL- differentiability | HL-differentiability | MS-differentiability | MATHEMATICS | Frechet differentiability

Fréchet differentiability | topological vector space | Mathematics, general | convex function | MS- differentiability | Mathematics | Minkowski function | balanced absorbing subset | HL- differentiability | HL-differentiability | MS-differentiability | MATHEMATICS | Frechet differentiability

Journal Article

Publications of the Research Institute for Mathematical Sciences, ISSN 0034-5318, 03/2000, Volume 36, Issue 1, pp. 139 - 157

We study the Banach *-algebra C-op(1)(I) of C-1-functions f on the compact interval I such that the corresponding Hilbert space operator function T --> f(T),...

MATHEMATICS | commutator equations | ALGEBRAS | Frechet derivative | INEQUALITY | VARIABLES | operator differentiability | C-center dot-algebra

MATHEMATICS | commutator equations | ALGEBRAS | Frechet derivative | INEQUALITY | VARIABLES | operator differentiability | C-center dot-algebra

Journal Article

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