Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2017, Volume 445, Issue 2, pp. 1267 - 1283

We present some extensions of classical results that involve elements of the dual of Banach spaces, such as Bishop–Phelp's theorem and James' compactness...

Weakly compact | James' compactness theorem | MATHEMATICS | WEAK COMPACTNESS | MATHEMATICS, APPLIED | BOUNDARIES | CONVEX-SETS

Weakly compact | James' compactness theorem | MATHEMATICS | WEAK COMPACTNESS | MATHEMATICS, APPLIED | BOUNDARIES | CONVEX-SETS

Journal Article

Journal of Convex Analysis, ISSN 0944-6532, 2018, Volume 25, Issue 4, pp. 1335 - 1344

The following result is proved: Let A be a convex bounded non weakly relatively compact subset of a Banach space E. We fix a convex weakly compact subset D of...

Weakly compact | James' compactness theorem | MATHEMATICS | weakly compact set | WEAK COMPACTNESS

Weakly compact | James' compactness theorem | MATHEMATICS | weakly compact set | WEAK COMPACTNESS

Journal Article

Annals of Global Analysis and Geometry, ISSN 0232-704X, 12/2018, Volume 54, Issue 4, pp. 541 - 549

In this paper, we prove a new Myers’ type diameter estimate on a complete connected Reimannian manifold which admits a bounded vector field such that the...

Geometry | Ricci soliton | Mathematical Physics | Analysis | 53C21 | Global Analysis and Analysis on Manifolds | Secondary 53C20 | Myers’ theorem | Mathematics | Bakry–Émery Ricci curvature | Differential Geometry | Primary 53C25 | MATHEMATICS | SOLITONS | Myers' theorem | MANIFOLDS | COMPACTNESS | Bakry-Emery Ricci curvature | Lower bounds | Curvature | Geodesy | Mathematics - Differential Geometry

Geometry | Ricci soliton | Mathematical Physics | Analysis | 53C21 | Global Analysis and Analysis on Manifolds | Secondary 53C20 | Myers’ theorem | Mathematics | Bakry–Émery Ricci curvature | Differential Geometry | Primary 53C25 | MATHEMATICS | SOLITONS | Myers' theorem | MANIFOLDS | COMPACTNESS | Bakry-Emery Ricci curvature | Lower bounds | Curvature | Geodesy | Mathematics - Differential Geometry

Journal Article

Topology and its Applications, ISSN 0166-8641, 02/2019, Volume 252, pp. 158 - 168

This manuscript extends both Cantor intersection theorem and Cantor–Kuratowski intersection theorem from the setting of metric spaces to the setting of...

Uniformizable space | Admissible space | Measure of noncompactness | Completeness | Compactness | Total boundedness | MATHEMATICS | ATTRACTORS | MATHEMATICS, APPLIED | SEMIGROUP ACTIONS | STABILITY

Uniformizable space | Admissible space | Measure of noncompactness | Completeness | Compactness | Total boundedness | MATHEMATICS | ATTRACTORS | MATHEMATICS, APPLIED | SEMIGROUP ACTIONS | STABILITY

Journal Article

Expositiones Mathematicae, ISSN 0723-0869, 2010, Volume 28, Issue 4, pp. 385 - 394

We show that the Arzelà–Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their...

Compactness in Lp | Kolmogorov–Riesz compactness theorem | Compactness in L | Kolmogorov-Riesz compactness theorem | MATHEMATICS | Compactness in L-P

Compactness in Lp | Kolmogorov–Riesz compactness theorem | Compactness in L | Kolmogorov-Riesz compactness theorem | MATHEMATICS | Compactness in L-P

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 10/2012, Volume 14, Issue 5, pp. 1250033 - 1250014

In 1983, Berestycki and Lions [Nonlinear scalar field equations I. Existence of a ground state, Arch. Ration. Mech. Anal.82 (1983) 313–346] studied the...

EXISTENCE | MATHEMATICS, APPLIED | SCALAR FIELD-EQUATIONS | NONLINEAR SCHRODINGER-EQUATIONS | POSITIVE SOLUTIONS | CONCENTRATION-COMPACTNESS PRINCIPLE | SEMILINEAR ELLIPTIC PROBLEMS | critical growth | Pohozaev identity | MATHEMATICS | R-N | Nonlinear scalar field equation | UNBOUNDED-DOMAINS | MOUNTAIN-PASS | ground state | Mountains | Energy levels | Arches | Infinity | Mathematical analysis | Ground state | Nonlinearity | Scalars

EXISTENCE | MATHEMATICS, APPLIED | SCALAR FIELD-EQUATIONS | NONLINEAR SCHRODINGER-EQUATIONS | POSITIVE SOLUTIONS | CONCENTRATION-COMPACTNESS PRINCIPLE | SEMILINEAR ELLIPTIC PROBLEMS | critical growth | Pohozaev identity | MATHEMATICS | R-N | Nonlinear scalar field equation | UNBOUNDED-DOMAINS | MOUNTAIN-PASS | ground state | Mountains | Energy levels | Arches | Infinity | Mathematical analysis | Ground state | Nonlinearity | Scalars

Journal Article

Expositiones Mathematicae, ISSN 0723-0869, 03/2019, Volume 37, Issue 1, pp. 84 - 91

The purpose of this short note is to provide a new and very short proof of a result by Sudakov (1957), offering an important improvement of the classical...

Kolmogorov–Riesz compactness theorem | Compactness in [formula omitted] | Compactness in L | MATHEMATICS | Kolmogorov-Riesz compactness theorem | Compactness in L-P | SPACES | Mathematics - Functional Analysis

Kolmogorov–Riesz compactness theorem | Compactness in [formula omitted] | Compactness in L | MATHEMATICS | Kolmogorov-Riesz compactness theorem | Compactness in L-P | SPACES | Mathematics - Functional Analysis

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2017, Volume 449, Issue 1, pp. 528 - 530

We provide a short proof of the following fact: If X is a Banach space, A and B are bounded, closed and convex sets with dist(A,B)>0 and every x⁎∈X⁎ with the...

Weakly compact sets | James' theorem | MATHEMATICS | MATHEMATICS, APPLIED | COMPACTNESS

Weakly compact sets | James' theorem | MATHEMATICS | MATHEMATICS, APPLIED | COMPACTNESS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2020, Volume 485, Issue 1, p. 123764

Let A be a closed, convex, bounded and non weakly compact subset of a Banach space E with 0∉A. Let us fix a convex and weakly compact subset W of E, a...

Reflexivity | Mackey topology | Weak compactness | Non attaining linear functionals | Risk measures | Lebesgue property | MATHEMATICS | MATHEMATICS, APPLIED | SETS

Reflexivity | Mackey topology | Weak compactness | Non attaining linear functionals | Risk measures | Lebesgue property | MATHEMATICS | MATHEMATICS, APPLIED | SETS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2019, Volume 470, Issue 1, pp. 279 - 291

For a vector measure m, with values in a Banach space, we analyze the localization of uniformly integrable subsets of scalar integrable functions with respect...

Uniform integrability | Vector measure | Compactness | Orlicz spaces | INTERPOLATION | MATHEMATICS | MATHEMATICS, APPLIED | RESPECT

Uniform integrability | Vector measure | Compactness | Orlicz spaces | INTERPOLATION | MATHEMATICS | MATHEMATICS, APPLIED | RESPECT

Journal Article

Annals of Applied Probability, ISSN 1050-5164, 06/2018, Volume 28, Issue 3, pp. 1379 - 1422

We study the behavior of second-order degenerate elliptic systems in divergence form with random coefficients which are stationary and ergodic. Assuming moment...

Degenerate elliptic system | Liouville theorem | Stochastic homogenization | Large-scale regularity | Degenerate elliptic equation | degenerate elliptic system | EQUATIONS | STATISTICS & PROBABILITY | HARMONIC-FUNCTIONS | large-scale regularity | INVARIANCE-PRINCIPLE | stochastic homogenization | COMPACTNESS METHODS

Degenerate elliptic system | Liouville theorem | Stochastic homogenization | Large-scale regularity | Degenerate elliptic equation | degenerate elliptic system | EQUATIONS | STATISTICS & PROBABILITY | HARMONIC-FUNCTIONS | large-scale regularity | INVARIANCE-PRINCIPLE | stochastic homogenization | COMPACTNESS METHODS

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 8/2019, Volume 58, Issue 4, pp. 1 - 13

We prove several classification results for p-Laplacian problems on bounded and unbounded domains, and deal with qualitative properties of sign-changing...

35J92 (35B33 · 35B53 · 35B38) | Mathematics | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | MATHEMATICS | EQUATIONS | MATHEMATICS, APPLIED | CLASSIFICATION | GLOBAL COMPACTNESS RESULT | REGULARITY

35J92 (35B33 · 35B53 · 35B38) | Mathematics | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | MATHEMATICS | EQUATIONS | MATHEMATICS, APPLIED | CLASSIFICATION | GLOBAL COMPACTNESS RESULT | REGULARITY

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2016, Volume 437, Issue 2, pp. 870 - 881

We prove an extension to the finitely additive setting of the theorem of Halmos and Savage. From this we deduce extensions of classical results of Drewnowski...

Yan theorem | Lebesgue decomposition | Halmos–Savage theorem | Weak compactness | Halmos-Savage theorem | MATHEMATICS | MATHEMATICS, APPLIED | LINEAR FUNCTIONALS | Mathematics - Probability

Yan theorem | Lebesgue decomposition | Halmos–Savage theorem | Weak compactness | Halmos-Savage theorem | MATHEMATICS | MATHEMATICS, APPLIED | LINEAR FUNCTIONALS | Mathematics - Probability

Journal Article

Journal of Intelligent and Fuzzy Systems, ISSN 1064-1246, 2019, Volume 36, Issue 6, pp. 6663 - 6668

In this paper, using the structures of (L, L)-fuzzy product supratopological spaces which were introduced by Hu Zhao and Gui-xiu Chen, we give a proof of...

Fuzzy compactness | Generalized Tychonoff theorem | Product topological spaces | (L M)-fuzzy supratopology | product topological spaces | fuzzy compactness | COMPACTNESS | generalized Tychonoff theorem | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | (L, M)-fuzzy supratopology | Theorems | Graphical user interface | Fuzzy

Fuzzy compactness | Generalized Tychonoff theorem | Product topological spaces | (L M)-fuzzy supratopology | product topological spaces | fuzzy compactness | COMPACTNESS | generalized Tychonoff theorem | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | (L, M)-fuzzy supratopology | Theorems | Graphical user interface | Fuzzy

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 01/2015, Volume 268, Issue 1, pp. 194 - 209

Let X and Y be Banach spaces and F⊂BY⁎. Endow Y with the topology τF of pointwise convergence on F. Assume that T:X⁎→Y is a bounded linear operator which is...

James sup theorem | The [formula omitted]-theorem | Boundary | The ℓ1-theorem | MATHEMATICS | WEAK COMPACTNESS | MINIMAX | BOUNDARIES | REFLEXIVITY | BALLS | BANACH-SPACES | The l-theorem | CONVEX-SETS

James sup theorem | The [formula omitted]-theorem | Boundary | The ℓ1-theorem | MATHEMATICS | WEAK COMPACTNESS | MINIMAX | BOUNDARIES | REFLEXIVITY | BALLS | BANACH-SPACES | The l-theorem | CONVEX-SETS

Journal Article

Journal of the Institute of Mathematics of Jussieu, ISSN 1474-7480, 04/2018, Volume 19, Issue 2, pp. 1 - 49

We prove a compactness theorem for metrics with bounded integral curvature on a fixed closed surface $\unicode[STIX]{x1D6F4}$. As a corollary we obtain a new...

differential geometry | compactness theorem | metric geometry | Alexandrov surfaces with bounded integral curvature | conical singularities | Theorems | Singularities | Integrals | Curvature

differential geometry | compactness theorem | metric geometry | Alexandrov surfaces with bounded integral curvature | conical singularities | Theorems | Singularities | Integrals | Curvature

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 10/2019, Volume 277, Issue 7, pp. 2092 - 2116

Let (M,g) be a compact Riemannian three-dimensional manifold with boundary. We prove the compactness of the set of scalar-flat metrics which are in the...

Compactness theorem | Mean curvature | Boundary Yamabe problem | Manifolds with boundary | YAMABE PROBLEM | EXISTENCE | PROOF | MATHEMATICS | CONFORMAL DEFORMATION | CURVATURE | BLOW-UP PHENOMENA | MANIFOLDS | EQUATION | UNIQUENESS THEOREMS

Compactness theorem | Mean curvature | Boundary Yamabe problem | Manifolds with boundary | YAMABE PROBLEM | EXISTENCE | PROOF | MATHEMATICS | CONFORMAL DEFORMATION | CURVATURE | BLOW-UP PHENOMENA | MANIFOLDS | EQUATION | UNIQUENESS THEOREMS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2017, Volume 452, Issue 2, pp. 1101 - 1127

Locally L0-convex modules were introduced in Filipovic et al. (2009) [10] as the analytic basis for the study of conditional risk measures. Later, the algebra...

Conditional convex risk measure | Stability properties | Locally [formula omitted]-convex module | James' compactness theorem | Conditionally locally convex space | Jouini–Schachermayer–Touzi theorem | Locally L | convex module

Conditional convex risk measure | Stability properties | Locally [formula omitted]-convex module | James' compactness theorem | Conditionally locally convex space | Jouini–Schachermayer–Touzi theorem | Locally L | convex module

Journal Article

Commentarii Mathematici Helvetici, ISSN 0010-2571, 2017, Volume 92, Issue 4, pp. 751 - 776

We prove that a sequence of Fueter sections of a bundle of compact hyperkähler manifolds $\mathfrak{X}$ over a 3-manifold $M$ with bounded energy converges...

Global analysis, analysis on manifolds | Differential geometry | Bubbling | Hyperkähler manifolds | Fueter sections | Compactness | MATHEMATICS | MAPS | bubbling | compactness | hyperkahler manifolds | GEOMETRY | Mathematics - Differential Geometry

Global analysis, analysis on manifolds | Differential geometry | Bubbling | Hyperkähler manifolds | Fueter sections | Compactness | MATHEMATICS | MAPS | bubbling | compactness | hyperkahler manifolds | GEOMETRY | Mathematics - Differential Geometry

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2018, Volume 460, Issue 2, pp. 682 - 702

Let X and Y be Banach spaces and let Ω be a compact Hausdorff space. By the classical Bartle–Dunford–Schwartz theorem, any operator S∈L(C(Ω),Y) admits an...

Operators on function spaces | Banach spaces | Operator-valued measure | p-Compactness | Integral representation | q-Semivariation | MATHEMATICS | MATHEMATICS, APPLIED | VALUED FUNCTION-SPACES | PRODUCTS | BANACH-SPACES | OPERATORS

Operators on function spaces | Banach spaces | Operator-valued measure | p-Compactness | Integral representation | q-Semivariation | MATHEMATICS | MATHEMATICS, APPLIED | VALUED FUNCTION-SPACES | PRODUCTS | BANACH-SPACES | OPERATORS

Journal Article

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