Journal of Global Optimization, ISSN 0925-5001, 3/2011, Volume 49, Issue 3, pp. 505 - 519

We provide a criterion giving a formula for the directional (or contingent) subdifferential of the difference of two convex functions. We even extend it to the...

Dissipative operator | Equi-subdifferentiability | Directional subdifferential | Fréchet subdifferential | Approximately pseudo-dissipative operator | Approximately convex function | 90C26 | Gap-continuity | Optimization | Economics / Management Science | Operations Research/Decision Theory | Approximately starshaped function | 26B05 | 26B25 | Computer Science, general | 49K27 | Real Functions | D.c.function | MATHEMATICS, APPLIED | FORMULA | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | Frechet subdifferential | DUALITY | OPTIMIZATION | OPTIMALITY CONDITIONS | Studies

Dissipative operator | Equi-subdifferentiability | Directional subdifferential | Fréchet subdifferential | Approximately pseudo-dissipative operator | Approximately convex function | 90C26 | Gap-continuity | Optimization | Economics / Management Science | Operations Research/Decision Theory | Approximately starshaped function | 26B05 | 26B25 | Computer Science, general | 49K27 | Real Functions | D.c.function | MATHEMATICS, APPLIED | FORMULA | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | Frechet subdifferential | DUALITY | OPTIMIZATION | OPTIMALITY CONDITIONS | Studies

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 7/2011, Volume 50, Issue 3, pp. 485 - 502

In this paper we first provide a general formula of inclusion for the Dini-Hadamard ε-subdifferential of the difference of two functions and show that it...

Fréchet ε -subdifferential | Cone-constrained nonsmooth nonconvex optimization problems | Optimality conditions in subdifferential form | Dini-Hadamard ε -subdifferential | Optimization | Economics / Management Science | Directionally approximately starshaped functions | 49J52 | Operations Research/Decision Theory | 90C56 | Sponge | Approximately starshaped functions | 26B25 | Computer Science, general | Real Functions | Dini-Hadamard ε-subdifferential | Fréchet ε-subdifferential | MATHEMATICS, APPLIED | APPROXIMATE SUBDIFFERENTIALS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Frechet epsilon-subdifferential | SUBGRADIENTS | CALCULUS | Cone-constrained nonsmooth nonconvex optimization problems Optimality conditions in subdifferential form | Dini-Hadamard epsilon-subdifferential | GRADIENTS | Computer science | Universities and colleges | Studies | Mathematical problems

Fréchet ε -subdifferential | Cone-constrained nonsmooth nonconvex optimization problems | Optimality conditions in subdifferential form | Dini-Hadamard ε -subdifferential | Optimization | Economics / Management Science | Directionally approximately starshaped functions | 49J52 | Operations Research/Decision Theory | 90C56 | Sponge | Approximately starshaped functions | 26B25 | Computer Science, general | Real Functions | Dini-Hadamard ε-subdifferential | Fréchet ε-subdifferential | MATHEMATICS, APPLIED | APPROXIMATE SUBDIFFERENTIALS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Frechet epsilon-subdifferential | SUBGRADIENTS | CALCULUS | Cone-constrained nonsmooth nonconvex optimization problems Optimality conditions in subdifferential form | Dini-Hadamard epsilon-subdifferential | GRADIENTS | Computer science | Universities and colleges | Studies | Mathematical problems

Journal Article

Hacettepe Journal of Mathematics and Statistics, ISSN 1303-5010, 2011, Volume 40, Issue 2, pp. 135 - 145

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 6/2016, Volume 90, Issue 3, pp. 569 - 580

The main objective of this article is to introduce a new class of real valued functions that include the well-known class of $${m}$$ m -convex functions...

Primary 26A51 | Secondary 39B12 | Analysis | Starshaped function | Mathematics | Combinatorics | {m}$$ m -convex function | Jensen convex function | m-convex function | MATHEMATICS | MATHEMATICS, APPLIED | Functions (mathematics) | Algebra | Mathematical analysis | Inequalities | Collection | Texts | Calculus | Formulas (mathematics)

Primary 26A51 | Secondary 39B12 | Analysis | Starshaped function | Mathematics | Combinatorics | {m}$$ m -convex function | Jensen convex function | m-convex function | MATHEMATICS | MATHEMATICS, APPLIED | Functions (mathematics) | Algebra | Mathematical analysis | Inequalities | Collection | Texts | Calculus | Formulas (mathematics)

Journal Article

Moroccan Journal of Pure and Applied Analysis, ISSN 2351-8227, 12/2017, Volume 3, Issue 2, pp. 140 - 148

The main objective of this research is to characterize all the real polynomial functions of degree less than the fourth which are Jensen -convex on the set of...

Jensen | convex function | Real polynomial function | starshaped function

Jensen | convex function | Real polynomial function | starshaped function

Journal Article

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, ISSN 1345-4773, 2017, Volume 18, Issue 8, pp. 1435 - 1457

In this paper, we introduce the notion of an almost phi(f)-contraction which involves generalized altering distance functions and then we prove the existence...

MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | BANACH OPERATOR PAIRS | strongly M-starshaped metric spaces | generalized altering distances | invariant approximation | GENERALIZED I-CONTRACTIONS | SUBWEAKLY COMMUTING MAPS | MATHEMATICS | INVARIANT APPROXIMATIONS | Common fixed point | THEOREMS | almost contraction | CIRIC-TYPE | SELFMAPS

MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | BANACH OPERATOR PAIRS | strongly M-starshaped metric spaces | generalized altering distances | invariant approximation | GENERALIZED I-CONTRACTIONS | SUBWEAKLY COMMUTING MAPS | MATHEMATICS | INVARIANT APPROXIMATIONS | Common fixed point | THEOREMS | almost contraction | CIRIC-TYPE | SELFMAPS

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2014, Volume 2014, Issue 1, pp. 1 - 33

This paper presents a survey that aims to provide a brief historical account of the development through the definitions and comparison of weaker forms of...

convex metric space | Mathematical and Computational Biology | best approximation | nonexpansive mapping | Mathematics | weakly compatible mappings | Topology | R -weakly commuting mappings | best simultaneous approximation | compatible mappings | Analysis | R -subcommuting | common fixed point | Mathematics, general | R -subweakly commuting mappings | Applications of Mathematics | Differential Geometry | starshaped set | Weakly compatible mappings | Common fixed point | Starshaped set | Best simultaneous approximation | R-subcommuting | R-weakly commuting mappings | Best approximation | Compatible mappings | Convex metric space | Nonexpansive mapping | R-subweakly commuting mappings | Fixed point theory | Usage | Convex functions | Metric spaces | Contraction operators

convex metric space | Mathematical and Computational Biology | best approximation | nonexpansive mapping | Mathematics | weakly compatible mappings | Topology | R -weakly commuting mappings | best simultaneous approximation | compatible mappings | Analysis | R -subcommuting | common fixed point | Mathematics, general | R -subweakly commuting mappings | Applications of Mathematics | Differential Geometry | starshaped set | Weakly compatible mappings | Common fixed point | Starshaped set | Best simultaneous approximation | R-subcommuting | R-weakly commuting mappings | Best approximation | Compatible mappings | Convex metric space | Nonexpansive mapping | R-subweakly commuting mappings | Fixed point theory | Usage | Convex functions | Metric spaces | Contraction operators

Journal Article

8.
Full Text
A Problem of Baernstein on the Equality of the p-Harmonic Measure of a Set and Its Closure

Proceedings of the American Mathematical Society, ISSN 0002-9939, 2/2006, Volume 134, Issue 2, pp. 509 - 519

A. Baernstein II (Comparison of p-harmonic measures of subsets of the unit circle, St. Petersburg Math. J. 9 (1998), 543-551, p. 548), posed the following...

Cubes | Eigenfunctions | Mathematical functions | Trace | Lipschitz domain | P-harmonic measure | Dirichlet problem | Ahlfors regular | P-harmonic function | Starshaped | Sobolev function | D-set | Unit disc | Minkowski dimension | MATHEMATICS, APPLIED | METRIC-SPACES | starshaped | unit disc | d-set | MATHEMATICS | trace | p-harmonic measure | p-harmonic function

Cubes | Eigenfunctions | Mathematical functions | Trace | Lipschitz domain | P-harmonic measure | Dirichlet problem | Ahlfors regular | P-harmonic function | Starshaped | Sobolev function | D-set | Unit disc | Minkowski dimension | MATHEMATICS, APPLIED | METRIC-SPACES | starshaped | unit disc | d-set | MATHEMATICS | trace | p-harmonic measure | p-harmonic function

Journal Article

Image Analysis & Stereology, ISSN 1580-3139, 05/2011, Volume 21, Issue 4, p. 23

This paper concerns the problem of making stereological inference about the shape variability in a population of spatial particles. Under rotational invariance...

spherical harmonics | Gaussian process | shape | Fourier descriptors | starshaped objects | stereology | radius-vector function

spherical harmonics | Gaussian process | shape | Fourier descriptors | starshaped objects | stereology | radius-vector function

Journal Article

Set-Valued Analysis, ISSN 0927-6947, 12/2008, Volume 16, Issue 4, pp. 413 - 427

We set up a formula for the Fréchet and ε-Fréchet subdifferentials of the difference of two convex functions. We even extend it to the difference of two...

Equi-subdifferentiability | Local minimizer | Fréchet subdifferential | Approximately convex function | Mathematics | ε -Fréchet subdifferential | 90C26 | Gap-continuity | Geometry | Function | Local blunt minimizer | Analysis | Approximately starshaped function | Blunt minimizer | d.c. Function | 26B05 | 26B25 | 49K27 | ε-Fréchet subdifferential | d.c. function | d.a.s. function | MATHEMATICS, APPLIED | epsilon-Frechet subdifferential | d.c Function | FORMULA | d.a.s Function | Frechet subdifferential | DUALITY | OPTIMIZATION | OPTIMALITY CONDITIONS

Equi-subdifferentiability | Local minimizer | Fréchet subdifferential | Approximately convex function | Mathematics | ε -Fréchet subdifferential | 90C26 | Gap-continuity | Geometry | Function | Local blunt minimizer | Analysis | Approximately starshaped function | Blunt minimizer | d.c. Function | 26B05 | 26B25 | 49K27 | ε-Fréchet subdifferential | d.c. function | d.a.s. function | MATHEMATICS, APPLIED | epsilon-Frechet subdifferential | d.c Function | FORMULA | d.a.s Function | Frechet subdifferential | DUALITY | OPTIMIZATION | OPTIMALITY CONDITIONS

Journal Article

Acta Scientiarum Mathematicarum, ISSN 0001-6969, 2014, Volume 80, Issue 3-4, pp. 689 - 699

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 06/2012, Volume 14, Issue 3, pp. 1250023 - 1250026

We prove that, if Ω is an open subset of ℝN with finite measure, there exists a hyperplane H through 0 such that the measure of Ω ∩ H is less than the measure...

functions of bounded variation | starshaped rearrangement | Isoperimetric inequalities | section by hyperplanes | Poincaré inequality | MATHEMATICS | MATHEMATICS, APPLIED | POINCARE | Poincare inequality | Equality | Mathematical analysis | Optimization | Hyperplanes | Inequalities

functions of bounded variation | starshaped rearrangement | Isoperimetric inequalities | section by hyperplanes | Poincaré inequality | MATHEMATICS | MATHEMATICS, APPLIED | POINCARE | Poincare inequality | Equality | Mathematical analysis | Optimization | Hyperplanes | Inequalities

Journal Article

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 04/2011, Volume 40, Issue 2, pp. 135 - 145

In this paper we establish new inequalities of Ostrowski type, for functions whose derivatives in absolute value are m-convex. We also give some applications...

Hermite-Hadamard inequality | Special means | Ostrowski inequality | Power Mean inequality | The midpoint formula | STATISTICS & PROBABILITY | Lipschitzian mapping | MATHEMATICS | DIFFERENTIABLE MAPPINGS | Holder inequality | Starshaped function | Convex function | m-convex function

Hermite-Hadamard inequality | Special means | Ostrowski inequality | Power Mean inequality | The midpoint formula | STATISTICS & PROBABILITY | Lipschitzian mapping | MATHEMATICS | DIFFERENTIABLE MAPPINGS | Holder inequality | Starshaped function | Convex function | m-convex function

Journal Article

Balkan Journal of Geometry and its Applications, ISSN 1224-2780, 2011, Volume 16, Issue 2, pp. 133 - 137

Let A be an open connected subset of a C-infinity complete simply connected 2-dimensional Riemannian manifold without conjugate points W-2. The main result of...

Maximal visibility | Conjugate points | Tietze-type theorem | Kernel | Starshaped set | MATHEMATICS | MATHEMATICS, APPLIED | maximal visibility | conjugate points | kernel | starshaped set | Manifolds (Mathematics) | Theorems (Mathematics) | Convex functions | Research

Maximal visibility | Conjugate points | Tietze-type theorem | Kernel | Starshaped set | MATHEMATICS | MATHEMATICS, APPLIED | maximal visibility | conjugate points | kernel | starshaped set | Manifolds (Mathematics) | Theorems (Mathematics) | Convex functions | Research

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 06/2017, Volume 108, Issue 6, pp. 621 - 624

In this note, we present a reverse isoperimetric inequality for embedded starshaped closed plane curves, which states that if K is a starshaped domain with...

Radial function | Reverse isoperimetric inequality | Starshaped curves | MATHEMATICS | Equality

Radial function | Reverse isoperimetric inequality | Starshaped curves | MATHEMATICS | Equality

Journal Article

IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 01/1999, Volume 21, Issue 1, pp. 31 - 41

A problem which often arises while fitting implicit polynomials to 2D and 3D data sets is the following: although the data set is simple, the fit exhibits...

Geometry | Pathology | Shape | Cost function | Surface fitting | Polynomials | Iterative algorithms | Curve fitting | Least squares approximation | Least squares methods | Toplogical integrity | Positive polynomials | Free-form shapes | Fitting | Starshaped curves and surfaces | Implicit polynomials | free-form shapes | starshaped curves and surfaces | ALGEBRAIC INVARIANTS | RECOGNITION | topological integrity | implicit polynomials | OBJECTS | fitting | positive polynomials | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Surfaces | Usage | Curves, Algebraic | Models | Geometry, Algebraic | Design engineering | Fittings | Topology | Ellipses | Pattern analysis | Optimization | Three dimensional | Heuristic

Geometry | Pathology | Shape | Cost function | Surface fitting | Polynomials | Iterative algorithms | Curve fitting | Least squares approximation | Least squares methods | Toplogical integrity | Positive polynomials | Free-form shapes | Fitting | Starshaped curves and surfaces | Implicit polynomials | free-form shapes | starshaped curves and surfaces | ALGEBRAIC INVARIANTS | RECOGNITION | topological integrity | implicit polynomials | OBJECTS | fitting | positive polynomials | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Surfaces | Usage | Curves, Algebraic | Models | Geometry, Algebraic | Design engineering | Fittings | Topology | Ellipses | Pattern analysis | Optimization | Three dimensional | Heuristic

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 05/2019, Volume 292, Issue 5, pp. 1008 - 1021

We study solutions of the problem 0.1 −(−Δ)α/2u=f(x,u)inD0∖D¯1,u=0inRN∖D0,u=1inD¯1, where D1,D0⊂RN are open sets such that D¯1⊂D0, α∈(0,2), and f is a...

35B06 | starshaped superlevel sets | 35B50 | fractional Laplacian | MATHEMATICS | LEVEL SETS | EXTERIOR | SYMMETRY | CONVEXITY | EIGENFUNCTION | DIRICHLET PROBLEM | BLOW-UP | HARMONIC FUNCTIONS

35B06 | starshaped superlevel sets | 35B50 | fractional Laplacian | MATHEMATICS | LEVEL SETS | EXTERIOR | SYMMETRY | CONVEXITY | EIGENFUNCTION | DIRICHLET PROBLEM | BLOW-UP | HARMONIC FUNCTIONS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2008, Volume 68, Issue 9, pp. 2750 - 2768

We study continuity properties of tangent and normal cones to a closed subset of a Banach space. Such a study can be seen as a nonsmooth set theoretic analogue...

Approximately convex set | Normal cone | Approximately starshaped function | Subdifferential | Approximately starshaped set | Softness | Approximately convex function | Sleekness | Regularity | Tangent cone | HILBERT-SPACES | MATHEMATICS, APPLIED | MEAN-VALUE THEOREM | approximately convex function | sleekness | regularity | CONVEX-FUNCTIONS | approximately starshaped function | MATHEMATICS | subdifferential | approximately convex set | PROXIMAL ANALYSIS | CLOSED-SETS | normal cone | DIRECTIONALLY LIPSCHITZIAN FUNCTIONS | approximately starshaped set | OPTIMIZATION | tangent cone | SUBDIFFERENTIABILITY SPACES | GRADIENTS | softness | BANACH-SPACE

Approximately convex set | Normal cone | Approximately starshaped function | Subdifferential | Approximately starshaped set | Softness | Approximately convex function | Sleekness | Regularity | Tangent cone | HILBERT-SPACES | MATHEMATICS, APPLIED | MEAN-VALUE THEOREM | approximately convex function | sleekness | regularity | CONVEX-FUNCTIONS | approximately starshaped function | MATHEMATICS | subdifferential | approximately convex set | PROXIMAL ANALYSIS | CLOSED-SETS | normal cone | DIRECTIONALLY LIPSCHITZIAN FUNCTIONS | approximately starshaped set | OPTIMIZATION | tangent cone | SUBDIFFERENTIABILITY SPACES | GRADIENTS | softness | BANACH-SPACE

Journal Article

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, ISSN 1534-0392, 11/2018, Volume 17, Issue 6, pp. 2729 - 2749

In this paper the author studies the isoperimetric problem in R-n with perimeter density |x|(p) and volume density 1. We settle completely the case n = 2;...

MATHEMATICS, APPLIED | case of equality | INEQUALITY | SOBOLEV | MATHEMATICS | starshaped domains | first variation | HYPERSURFACES | REGIONS | Isoperimetric problem with density | EXTREMAL-FUNCTIONS | WEIGHTS | radial weight | 2 DIMENSIONS

MATHEMATICS, APPLIED | case of equality | INEQUALITY | SOBOLEV | MATHEMATICS | starshaped domains | first variation | HYPERSURFACES | REGIONS | Isoperimetric problem with density | EXTREMAL-FUNCTIONS | WEIGHTS | radial weight | 2 DIMENSIONS

Journal Article

Statistics and Probability Letters, ISSN 0167-7152, 04/2013, Volume 83, Issue 4, pp. 1036 - 1045

In this paper, we consider the comparison of parametric families of income distributions in terms of inequality and relative deprivation, which are two...

Lorenz orders | Gamma generalized distribution | Type I and II Beta generalized distributions | Starshaped, expected proportional shortfall | Inequality | STATISTICS & PROBABILITY | GENERALIZED-FUNCTIONS | SIZE DISTRIBUTION | Comparative analysis | Family

Lorenz orders | Gamma generalized distribution | Type I and II Beta generalized distributions | Starshaped, expected proportional shortfall | Inequality | STATISTICS & PROBABILITY | GENERALIZED-FUNCTIONS | SIZE DISTRIBUTION | Comparative analysis | Family

Journal Article

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