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2014, De Gruyter studies in mathematics, ISBN 9783110281231, Volume 52., xiii, 449
Book
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
Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2019, Volume 71, Issue 1, pp. 91 - 115
Let L-1 and L-2 be nonnegative self-adjoint operators acting on L-2(X-1) and L-2 (X-2), respectively, where X-1 and X-2 are spaces of homogeneous type. Assume... 
MATHEMATICS | DUALITY | BESOV-LIPSCHITZ | BMO
Journal Article
Fuzzy Sets and Systems, ISSN 0165-0114, 11/2017, Volume 326, pp. 89 - 105
We introduce and study transformations that assign to each conjunctive real-valued function F:[0,1]2→R and any pair of parameters (a,b)∈[0,1]2 a function... 
Quasi-copula | Copula | Spearman's rho | Conjunctive function | Kendall's tau | Tail dependence parameters | Measure-preserving transformation | Lipschitz conjunctive function | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | DIAGONAL SECTIONS | PATCHWORK | QUASI-COPULAS | CONSTRUCTIONS | COMPUTER SCIENCE, THEORY & METHODS | BIVARIATE COPULAS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2017, Volume 448, Issue 1, pp. 447 - 472
For a Banach function algebra A, we consider the problem of representing a continuous d-homogeneous polynomial P:A→X, where X is an arbitrary Banach space,... 
Algebra of Lipschitz functions | Figà–Talamanca–Herz algebra | Orthogonally additive polynomial | Algebra of absolutely continuous functions | Algebra of differentiable functions | Fourier algebra | Figa-Talamanca-Herz algebra | MATHEMATICS, APPLIED | SPACES | DERIVATIONS | MATHEMATICS | MAPS | HOLOMORPHIC-FUNCTIONS | HYPERREFLEXIVITY | Algebra
Journal Article
Journal of Optimization Theory and Applications, ISSN 0022-3239, 11/2016, Volume 171, Issue 2, pp. 481 - 503
Journal Article
Formalized Mathematics, ISSN 1898-9934, 12/2017, Volume 25, Issue 4, pp. 269 - 281
In this article, we formalize in Mizar [1], [3] the existence and uniqueness part of the implicit function theorem. In the first section, some composition... 
version: 8.1.06 5.45.1311 | identifier: NDIFF 8 | 26B10 53A07 03B35 | Banach fixed point theorem | implicit function theorem | Lipschitz continuity
Journal Article
Formalized Mathematics, ISSN 1426-2630, 07/2019, Volume 27, Issue 2, pp. 117 - 131
In this article, we formalize differentiability of implicit function theorem in the Mizar system [3], [1]. In the first half section, properties of Lipschitz... 
differentiability | 47A05 | 26B10 | 47J07 | 53A07 | implicit function | 03B35 | implicit function theorem | Lipschitz continuity | lipschitz continuity | 47a05 | 26b10 | 47j07 | 53a07 | 03b35
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2018, Volume 461, Issue 2, pp. 1287 - 1298
Under the right conditions on a compact metric space X and on a Banach space E, we give a description of the 2-local (standard) isometries on the Banach space... 
Lipschitz function | Isometry | 2-iso-reflexive | 2-local isometry | VON-NEUMANN-ALGEBRAS | MATHEMATICS | MATHEMATICS, APPLIED | WEAK-2-LOCAL DERIVATIONS | THEOREM | B(H) | AUTOMORPHISMS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2016, Volume 444, Issue 1, pp. 210 - 229
We give a characterization of algebra homomorphisms and isomorphisms between Banach algebras of Lipschitz functions with the values in unital commutative... 
Unital commutative [formula omitted]-algebras | Algebra homomorphisms | Banach algebras of Lipschitz functions | Algebra isomorphisms | algebras | Unital commutative C | MATHEMATICS | MATHEMATICS, APPLIED | REFLEXIVITY | Unital commutative C-algebras | Algebra
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 08/2018, Volume 291, Issue 11-12, pp. 1899 - 1907
In this article, we describe isometries over the Lipschitz spaces under certain conditions. Indeed, we provide a unified proof for the main results of and in a... 
46E40; Secondary: 46E15 | algebra isomorphism | Banach–Stone theorem | Primary: 46B04 | multipliers | Lipschitz maps | isometry | MATHEMATICS | METRIC-SPACES | BANACH-STONE-THEOREM | Banach-Stone theorem
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 10/2019, Volume 277, Issue 8, pp. 2697 - 2727
We develop tools for proving isomorphisms of normed spaces of Lipschitz functions over various doubling metric spaces and Banach spaces. In particular, we show... 
Lipschitz functions | Lipschitz-free spaces | Orlicz spaces | Carnot groups | MATHEMATICS | SEPARATED NETS | THEOREM | PROPERTY | METRICS | GROWTH | Analysis | Numerical analysis
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 04/2015, Volume 21, Issue 1-3, pp. 99 - 111
Journal Article
Communications on Pure and Applied Mathematics, ISSN 0010-3640, 08/2014, Volume 67, Issue 8, pp. 1219 - 1262
For a family of second‐order elliptic operators with rapidly oscillating periodic coefficients, we study the asymptotic behavior of the Green and Neumann... 
MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | DIRICHLET PROBLEM | LIPSCHITZ-DOMAINS | DIVERGENCE FORM | EQUATION | SINGULAR-INTEGRALS | COMPACTNESS METHODS
Journal Article
Advances in Mathematics, ISSN 0001-8708, 2010, Volume 224, Issue 3, pp. 910 - 966
It is well known that a Lipschitz function on the real line does not have to be operator Lipschitz. We show that the situation changes dramatically if we pass... 
Operator Hölder functions | Multiple operator integrals | Contractions | Hölder classes | Zygmund class | Unitary operators | Operator Lipschitz function | Self-adjoint operators | Holder classes | INTEGRALS | MATHEMATICS | Operator Holder functions | LIPSCHITZ
Journal Article
Optimization Letters, ISSN 1862-4472, 12/2018, Volume 12, Issue 8, pp. 1971 - 1980
We say that a positively homogeneous function admits a saddle representation by linear functions iff it admits both an inf-sup-representation and a... 
Difference sublinear functions | Positively homogeneous functions | Saddle representation | Lipschitz continuity | Piecewise linear functions | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Journal Article