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 (X1×X2...

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

Topology and its Applications, ISSN 0166-8641, 2012, Volume 159, Issue 1, pp. 183 - 193

Let ( X , τ ) be a topological space and let ρ be a metric defined on X. We shall say that ( X , τ ) is fragmented by ρ if whenever ε > 0 and A is a nonempty subset of X there is a...

Fragmentable | σ-Fragmentable | Function spaces | Topological groups | MATHEMATICS, APPLIED | NORMS | WEAK ASPLUND | MATHEMATICS | CONTINUITY | SIGMA-FRAGMENTABILITY | CONTINUOUS-MAPPINGS | sigma-Fragmentable | BANACH-SPACES | RADON-NIKODYM PROPERTY | SETS | OPTIMIZATION | ASPLUND SPACES

Fragmentable | σ-Fragmentable | Function spaces | Topological groups | MATHEMATICS, APPLIED | NORMS | WEAK ASPLUND | MATHEMATICS | CONTINUITY | SIGMA-FRAGMENTABILITY | CONTINUOUS-MAPPINGS | sigma-Fragmentable | BANACH-SPACES | RADON-NIKODYM PROPERTY | SETS | OPTIMIZATION | ASPLUND SPACES

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 09/2006, Volume 134, Issue 9, pp. 2745 - 2754

In this paper we construct a Gâteaux differentiability space that is not a weak Asplund space...

Unit ball | Topological theorems | Homeomorphism | Differential topology | Mathematical functions | Metric spaces | Topology | Banach space | Topological spaces | Weak Asplund space | Gâteaux differentiability space | Stegall space | MATHEMATICS | MATHEMATICS, APPLIED | Gateaux differentiability space | weak Asplund space

Unit ball | Topological theorems | Homeomorphism | Differential topology | Mathematical functions | Metric spaces | Topology | Banach space | Topological spaces | Weak Asplund space | Gâteaux differentiability space | Stegall space | MATHEMATICS | MATHEMATICS, APPLIED | Gateaux differentiability space | weak Asplund space

Journal Article

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ESSENTIAL SMOOTHNESS, ESSENTIAL STRICT CONVEXITY, AND LEGENDRE FUNCTIONS IN BANACH SPACES

Communications in Contemporary Mathematics, ISSN 0219-1997, 11/2001, Volume 3, Issue 4, pp. 615 - 647

The classical notions of essential smoothness, essential strict convexity, and Legendreness for convex functions are extended from Euclidean to Banach spaces...

Convex function of Legendre type | Bregman distance, Bregman projection | Cofinite function | Schur property | Schur space | Subdifferential | Weak Asplund space | Essentially smooth | Essentially strictly convex | Legendre function | Supercoercive | Coercive | MATHEMATICS, APPLIED | weak Asplund space | cofinite function | zone consistent | convex function of Legendre type | essentially strictly convex | Bregman distance | supercoercive | Bregman projection | MATHEMATICS | subdifferential | essentially smooth | coercive | Mathematical optimization | Analysis | Algorithms

Convex function of Legendre type | Bregman distance, Bregman projection | Cofinite function | Schur property | Schur space | Subdifferential | Weak Asplund space | Essentially smooth | Essentially strictly convex | Legendre function | Supercoercive | Coercive | MATHEMATICS, APPLIED | weak Asplund space | cofinite function | zone consistent | convex function of Legendre type | essentially strictly convex | Bregman distance | supercoercive | Bregman projection | MATHEMATICS | subdifferential | essentially smooth | coercive | Mathematical optimization | Analysis | Algorithms

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 02/2003, Volume 131, Issue 2, pp. 647 - 654

A topological space X is said to belong to the class of Stegall (weakly Stegall) spaces if for every Baire (complete metric...

Topological theorems | Abstract spaces | Completely regular spaces | Compactification | Metric spaces | Mathematical functions | Topology | Banach space | Topological spaces | Weak Asplund | Weakly Stegall space | Almost weak Asplund | Stegall space | MATHEMATICS | almost weak Asplund | MATHEMATICS, APPLIED | weak Asplund | weakly Stegall space

Topological theorems | Abstract spaces | Completely regular spaces | Compactification | Metric spaces | Mathematical functions | Topology | Banach space | Topological spaces | Weak Asplund | Weakly Stegall space | Almost weak Asplund | Stegall space | MATHEMATICS | almost weak Asplund | MATHEMATICS, APPLIED | weak Asplund | weakly Stegall space

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2003, Volume 197, Issue 1, pp. 1 - 13

We prove that a dual Banach space X ∗ has an equivalent W ∗ LUR norm if and only if the weak ∗ topology has a σ-isolated network...

Sigma-isolated network | Weak locally uniformly rotund norms | Weak Asplund Banach spaces | Smooth renorming of Banach spaces | Fragmentable and descriptive spaces | MATHEMATICS | weak locally uniformly rotund norms | weak Asplund Banach spaces | sigma-isolated network | smooth renorming of Banach spaces | BANACH-SPACES | fragmentable and descriptive spaces

Sigma-isolated network | Weak locally uniformly rotund norms | Weak Asplund Banach spaces | Smooth renorming of Banach spaces | Fragmentable and descriptive spaces | MATHEMATICS | weak locally uniformly rotund norms | weak Asplund Banach spaces | sigma-isolated network | smooth renorming of Banach spaces | BANACH-SPACES | fragmentable and descriptive spaces

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2013, Volume 405, Issue 1, pp. 297 - 309

In this article, we begin using some geometric methods to study the isometric extension problem in general real Banach spaces...

Asplund generated space | Weak∗-exposed point | Isometric extension | Weak-Asplund space | Sharp corner point | Weakly compactly generated space | Gâteaux differentiable space | Weak | exposed point | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | L-INFINITY | MATHEMATICS | Weak-exposed point | P-SPACES | NORMED SPACE | Gateaux differentiable space | REPRESENTATION THEOREM | HILBERT-SPACE | 2 UNIT SPHERES

Asplund generated space | Weak∗-exposed point | Isometric extension | Weak-Asplund space | Sharp corner point | Weakly compactly generated space | Gâteaux differentiable space | Weak | exposed point | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | L-INFINITY | MATHEMATICS | Weak-exposed point | P-SPACES | NORMED SPACE | Gateaux differentiable space | REPRESENTATION THEOREM | HILBERT-SPACE | 2 UNIT SPHERES

Journal Article

Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 04/2015, Volume 91, Issue 2, pp. 303 - 310

In a recent paper, topological spaces $(X,{\it\tau})$ that are fragmented by a metric that generates the discrete topology were investigated...

Fragmentable | Sigma-scattered | Topological game | WEAK ASPLUND SPACE | MATHEMATICS | sigma-scattered | CONTINUITY | SIGMA-FRAGMENTABILITY | CONTINUOUS-MAPPINGS | BANACH-SPACES | RADON-NIKODYM PROPERTY | NORM | OPTIMIZATION | DIFFERENTIATION | fragmentable | topological game

Fragmentable | Sigma-scattered | Topological game | WEAK ASPLUND SPACE | MATHEMATICS | sigma-scattered | CONTINUITY | SIGMA-FRAGMENTABILITY | CONTINUOUS-MAPPINGS | BANACH-SPACES | RADON-NIKODYM PROPERTY | NORM | OPTIMIZATION | DIFFERENTIATION | fragmentable | topological game

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 12/2001, Volume 129, Issue 12, pp. 3741 - 3747

Under the assumption that there exists in the unit interval [0,1] an uncountable set A with the property that every continuous mapping from a Baire metric space...

Unit ball | Topological theorems | Homeomorphism | Mathematical functions | Topology | Banach space | Topological spaces | Continuous functions | Weak asplund space | Baire space | Double arrow space | Stegall's class | Minimal usco | Fragmentability | fragmentability | MATHEMATICS | MATHEMATICS, APPLIED | weak Asplund space | double arrow space | minimal usco

Unit ball | Topological theorems | Homeomorphism | Mathematical functions | Topology | Banach space | Topological spaces | Continuous functions | Weak asplund space | Baire space | Double arrow space | Stegall's class | Minimal usco | Fragmentability | fragmentability | MATHEMATICS | MATHEMATICS, APPLIED | weak Asplund space | double arrow space | minimal usco

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 02/2005, Volume 133, Issue 2, pp. 425 - 429

Assuming the consistency of the existence of a measurable cardinal, it is consistent to have two Banach spaces, X,Y, where X is a weak Asplund space such that X^{*} (in the weak* topology...

Mathematical set theory | Mathematical theorems | Kalinda | Axioms | Mathematical analysis | Mathematical functions | Banach space | Topological spaces | Weak Asplund space | Fragmentable space | Measurable cardinal | Stegall's class of spaces | MATHEMATICS | measurable cardinal | MATHEMATICS, APPLIED | weak Asplund space | COHEN EXTENSIONS | fragmentable space | PRECIPITOUS IDEALS

Mathematical set theory | Mathematical theorems | Kalinda | Axioms | Mathematical analysis | Mathematical functions | Banach space | Topological spaces | Weak Asplund space | Fragmentable space | Measurable cardinal | Stegall's class of spaces | MATHEMATICS | measurable cardinal | MATHEMATICS, APPLIED | weak Asplund space | COHEN EXTENSIONS | fragmentable space | PRECIPITOUS IDEALS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 07/2002, Volume 130, Issue 7, pp. 2139 - 2143

We show that, under some additional set-theoretical assumptions which are equiconsistent with the existence of a measurable cardinal, there is a weak Asplund space whose dual, equipped with the weak...

Mathematical theorems | Kalinda | Martins axiom | Mathematics | Mathematical functions | Local extrema | Banach space | Continuum hypothesis | Topological spaces | Continuous functions | Weak Asplund space | Fragmentable space | Stegall's class of spaces | MATHEMATICS | MATHEMATICS, APPLIED | weak Asplund space | fragmentable space

Mathematical theorems | Kalinda | Martins axiom | Mathematics | Mathematical functions | Local extrema | Banach space | Continuum hypothesis | Topological spaces | Continuous functions | Weak Asplund space | Fragmentable space | Stegall's class of spaces | MATHEMATICS | MATHEMATICS, APPLIED | weak Asplund space | fragmentable space

Journal Article

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, ISSN 1345-4773, 2017, Volume 18, Issue 10, pp. 1867 - 1882

In this paper, some necessary and sufficient conditions for Gateaux differentiability of w*-lower semicontinuous convex function of X** are given. Moreover, we...

MATHEMATICS | MATHEMATICS, APPLIED | Asplund space | ball-covering property | WEAK ASPLUND | convex function | FRECHET DIFFERENTIABILITY | Gateaux differentiability

MATHEMATICS | MATHEMATICS, APPLIED | Asplund space | ball-covering property | WEAK ASPLUND | convex function | FRECHET DIFFERENTIABILITY | Gateaux differentiability

Journal Article

STUDIA MATHEMATICA, ISSN 0039-3223, 2008, Volume 184, Issue 3, pp. 249 - 262

We consider the class of compact spaces K-A which are modifications of the well known double arrow space...

MATHEMATICS | BAIRE CLASS FUNCTIONS | COMPACT SPACES | CLASSIFICATION | WEAK ASPLUND SPACE | SETS

MATHEMATICS | BAIRE CLASS FUNCTIONS | COMPACT SPACES | CLASSIFICATION | WEAK ASPLUND SPACE | SETS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 10/1987, Volume 303, Issue 2, pp. 517 - 527

We show that, typically, lower semicontinuous functions on a Banach space densely inherit lower subderivatives of the same degree of smoothness as the norm...

Mathematical theorems | Nonsmooth analysis | Hilbert spaces | Mathematical functions | Mathematical inequalities | Banach space | Distance functions | Ekeland’s principle | Proximal normals | Weak Asplund spaces | Renorms | Sub derivatives

Mathematical theorems | Nonsmooth analysis | Hilbert spaces | Mathematical functions | Mathematical inequalities | Banach space | Distance functions | Ekeland’s principle | Proximal normals | Weak Asplund spaces | Renorms | Sub derivatives

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 4/1992, Volume 114, Issue 4, pp. 1003 - 1008

The techniques of Preiss-Phelps-Namioka is used to prove that if a Banach space E admits...

Integers | Frechet topologies | Mathematical theorems | Topological theorems | Mathematical functions | Banach space | Topological spaces | Weak Asplund spaces | Fragmentability | MATHEMATICS | FRAGMENTABILITY | MATHEMATICS, APPLIED | WEAK ASPLUND SPACES | NIKODYM

Integers | Frechet topologies | Mathematical theorems | Topological theorems | Mathematical functions | Banach space | Topological spaces | Weak Asplund spaces | Fragmentability | MATHEMATICS | FRAGMENTABILITY | MATHEMATICS, APPLIED | WEAK ASPLUND SPACES | NIKODYM

Journal Article

Set-Valued Analysis, ISSN 0927-6947, 3/2004, Volume 12, Issue 1, pp. 49 - 60

... for every proper lower semicontinuous extended real-valued function f defined on a metric space X...

Geometry | variational principle | separable Banach space | well-posed optimization problem | weak Asplund space | Analysis | perturbed optimization problem | Mathematics | Gâteaux differentiability space | Weak Asplund space | Well-posed optimization problem | Separable Banach space | Perturbed optimization problem | Variational principle | SPACE | MATHEMATICS, APPLIED | DIFFERENTIABILITY | Gateaux differentiability space | OPTIMIZATION

Geometry | variational principle | separable Banach space | well-posed optimization problem | weak Asplund space | Analysis | perturbed optimization problem | Mathematics | Gâteaux differentiability space | Weak Asplund space | Well-posed optimization problem | Separable Banach space | Perturbed optimization problem | Variational principle | SPACE | MATHEMATICS, APPLIED | DIFFERENTIABILITY | Gateaux differentiability space | OPTIMIZATION

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 7/1988, Volume 103, Issue 3, pp. 773 - 778

...)$ of nonsupport points of a closed convex subset $C$ of a Banach space $E$, which is assumed to be either an Asplund space...

Hausdorff spaces | Rain | Mathematical theorems | Maps | Mathematical functions | Banach space | Topological spaces | Weak Asplund spaces | Convex sets | Asplund spaces | Convex functions | Support points | Usco maps

Hausdorff spaces | Rain | Mathematical theorems | Maps | Mathematical functions | Banach space | Topological spaces | Weak Asplund spaces | Convex sets | Asplund spaces | Convex functions | Support points | Usco maps

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 9/1990, Volume 110, Issue 1, pp. 117 - 123

Subdifferentials of convex functions and some regular functions f are expressed in terms of limiting gradients at points in a given dense subset of .

Banach space | Directional derivatives | Mathematical functions | Directionally Lipschitz functions | Weak Asplund spaces | Pseudoregular functions | MATHEMATICS | MATHEMATICS, APPLIED

Banach space | Directional derivatives | Mathematical functions | Directionally Lipschitz functions | Weak Asplund spaces | Pseudoregular functions | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Set-Valued Analysis, ISSN 0927-6947, 12/2001, Volume 9, Issue 4, pp. 383 - 390

... (2000): 28A35, 46E15, 46E47, 46N10, 47H05, 90C48. Key words: general Monge–Kantorovich problem, Borel measure, support function, subdifferential, space...

Geometry | subdifferential | weak Asplund space | support function | Analysis | Mathematics | Borel measure | space of continuous functions | general Monge-Kantorovich problem | Weak Asplund space | Support function | General Monge-Kantorovich problem | Subdifferential | Space of continuous functions | MATHEMATICS, APPLIED

Geometry | subdifferential | weak Asplund space | support function | Analysis | Mathematics | Borel measure | space of continuous functions | general Monge-Kantorovich problem | Weak Asplund space | Support function | General Monge-Kantorovich problem | Subdifferential | Space of continuous functions | MATHEMATICS, APPLIED

Journal Article

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