Matrix inequalities between $$f(A)\sigma f(B)$$ and $$A\sigma B$$: Matrix inequalities between \(f(A)\sigma f(B)\) and \(A\sigma B\)

Authors: Devi, Manisha, Aujla, Jaspal Singh, Kian, Mohsen, Moslehian, Mohammad Sal

Source: Aequationes mathematicae. 99:539-554

Subject Terms: convex function, Mathematics - Functional Analysis, Miscellaneous inequalities involving matrices, unitarily invariant norm, matrix mean, Norms of matrices, numerical range, applications of functional analysis to matrix theory, concave function, Determinants, permanents, traces, other special matrix functions, determinant inequality, 15A60, 15A42, Convexity of real functions of several variables, generalizations

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Access URL: http://arxiv.org/abs/2302.08127

The dual $$p$$-convex functions and its applications: The dual \(p\)-convex functions and its applications

Authors: Rigao He, Wei Wang

Source: Calculus of Variations and Partial Differential Equations. 64

Subject Terms: Inequalities and extremum problems involving convexity in convex geometry, Inequalities involving derivatives and differential and integral operators, Convexity of real functions of several variables, generalizations

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Approximate weak efficiency of the set-valued optimization problem with variable ordering structures

Authors: Zhiang Zhou, Wenbin Wei, Fei Huang, Kequan Zhao

Source: Journal of Combinatorial Optimization. 48

Subject Terms: scalarization, set-valued maps, approximate weakly efficient solution, variable ordering structures, Optimality conditions and duality in mathematical programming, Nonconvex programming, global optimization, Multi-objective and goal programming, Convexity of real functions of several variables, generalizations, Set-valued and variational analysis

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Recent progress on integrally convex functions

Authors: Kazuo Murota, Akihisa Tamura

Source: Japan Journal of Industrial and Applied Mathematics. 40:1445-1499

Subject Terms: Convex programming, Combinatorial optimization, integrally convex function, 0211 other engineering and technologies, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, Fenchel duality, integral subgradient, FOS: Mathematics, discrete convex analysis, Mathematics - Combinatorics, minimization, box-total dual integrality, Combinatorics (math.CO), 52A41, 90C10, 90C25, Convexity of real functions of several variables, generalizations

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Access URL: http://arxiv.org/abs/2211.10912

About the B-concavity of functions with many variables

Authors: Meleşteu Alexandra Diana

Source: Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, Vol 31, Iss 1, Pp 199-206 (2023)

Subject Terms: b concavity, Multidimensional problems, Approximation by positive operators, Bernstein operators, B concavity, 26b25, bernstein operators, BB-concavity, QA1-939, bb-concavity, 41a63, 41a36, Mathematics, Convexity of real functions of several variables, generalizations

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Access URL: https://zbmath.org/8036471
https://doi.org/10.2478/auom-2023-0010
https://doaj.org/article/4b2f838dbe78480e8e039c8a74e74867

Hierarchy of deformations in concavity

Authors: Ishige K., Salani P., Takatsu A.

Source: Information Geometry. 7:251-269

Subject Terms: Deformation, Deformed logarithmic function, Generalized concavity, deformed logarithmic function, deformation, generalized concavity, hierarchy, 0101 mathematics, 01 natural sciences, Convexity of real functions of several variables, generalizations, Means

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Access URL: https://zbmath.org/7789554
https://doi.org/10.1007/s41884-022-00088-4

Approximate Benson properly efficient solutions for set-valued equilibrium problems

Authors: Zhou, Zhiang, Huang, Fei, Ansari, Qamrul Hasan

Source: Positivity. 28

Subject Terms: scalarization, set-valued equilibrium problem, nonemptiness, Optimality conditions and duality in mathematical programming, approximate Benson properly efficient solution, Nonconvex programming, global optimization, Multi-objective and goal programming, connectedness, Convexity of real functions of several variables, generalizations

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Arcwise-convex functions on surfaces

Authors: Rapcsák, T.

Source: Publicationes Mathematicae Debrecen. 34:35-41

Subject Terms: Nonlinear programming, differential geometry, 0101 mathematics, second-order necessary and sufficient conditions, 01 natural sciences, arcwise-convex functions, Convexity of real functions of several variables, generalizations

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Access URL: https://zbmath.org/4031419

A convex function satisfying the Łojasiewicz inequality but failing the gradient conjecture both at zero and infinity

Authors: Daniilidis, Aris, Haddou, Mounir, Ley, Olivier

Contributors: Ley, Olivier, Center for Mathematical Modeling (CMM), Universidad de Chile = University of Chile Santiago (UCHILE), Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011)

Source: Bulletin of the London Mathematical Society. 54:590-608

Subject Terms: convex function, Geometric methods in ordinary differential equations, Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.), [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Dynamical Systems (math.DS), 01 natural sciences, Real-analytic functions, Convex functions and convex programs in convex geometry, Optimization and Control (math.OC), FOS: Mathematics, convergence of secants, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Dynamical Systems, 0101 mathematics, gradient conjecture at infinity, Gradient conjecture, Mathematics - Optimization and Control, Kurdyka-Lojasiewicz inequality, Convexity of real functions of several variables, generalizations

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Access URL: http://arxiv.org/abs/2102.05342
https://zbmath.org/7729782
https://doi.org/10.1112/blms.12586
https://hal.science/hal-03136550v2
https://hal.science/hal-03136550v2/document
https://doi.org/10.1112/blms.12586

On Strongly Generalized Preinvex Fuzzy Mappings: On strongly generalized preinvex fuzzy mappings

Authors: Peide Liu, Muhammad Bilal Khan, Muhammad Aslam Noor, Khalida Inayat Noor

Source: Journal of Mathematics, Vol 2021 (2021)

Subject Terms: Fuzzy real analysis, QA1-939, 0202 electrical engineering, electronic engineering, information engineering, 02 engineering and technology, 0101 mathematics, 01 natural sciences, Mathematics, 6. Clean water, Convexity of real functions of several variables, generalizations

File Description: application/xml; text/xhtml

Access URL: https://downloads.hindawi.com/journals/jmath/2021/6657602.pdf
https://zbmath.org/7361867
https://doi.org/10.1155/2021/6657602
https://doaj.org/article/62d8dc14da144c748df9238364664ce1
https://www.hindawi.com/journals/jmath/2021/6657602/
https://downloads.hindawi.com/journals/jmath/2021/6657602.pdf
http://downloads.hindawi.com/journals/jmath/2021/6657602.pdf

Some integral inequalities for generalized preinvex functions with applications

Authors: Muhammad Tariq, Soubhagya Kumar Sahoo, Fahd Jarad, Bibhakar Kodamasingh

Source: AIMS Mathematics, Vol 6, Iss 12, Pp 13907-13930 (2021)

Subject Terms: Algebraic number, Hölder inequality, Evolutionary biology, hölder-i̇şcan inequality, Convex Functions, Matrix Inequalities and Geometric Means, Mathematical analysis, Quantum mechanics, 01 natural sciences, Convexity of real functions in one variable, generalizations, Orthogonal Polynomials, Fractional derivatives and integrals, Nonlinear programming, \(s\)-type preinvexity, Field (mathematics), QA1-939, improved power-mean integral inequality, FOS: Mathematics, Hölder-İşcan inequality, 0101 mathematics, Biology, Hadamard transform, hölder's inequality, Convexity of real functions of several variables, generalizations, s-type preinvexity, Hermite polynomials, Algebra over a field, Arithmetic, Ecology, Applied Mathematics, Physics, Matrix Inequalities, Pure mathematics, Harmonic, Stability of Functional Equations in Mathematical Analysis, Inequality, Function (biology), FOS: Biological sciences, Physical Sciences, Inequalities for sums, series and integrals, Hermite-Hadamard Inequalities, Type (biology), Mathematics, preinvex function, Hypergeometric Functions

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Access URL: https://doaj.org/article/f4a70905a802439d85056fab9698c293
https://www.aimspress.com/article/doi/10.3934/math.2021805

Weak sharp solutions associated with a multidimensional variational-type inequality

Authors: Savin Treanţă, Shipra Singh

Source: Positivity. 25:329-351

Subject Terms: \((\rho,\mathbf{b,d})\)-convex multiple integral functional, Numerical optimization and variational techniques, Nonlinear programming, continuous optimization, 0211 other engineering and technologies, Optimality conditions for problems involving partial differential equations, extended multidimensional variational-type inequality, 02 engineering and technology, Variational inequalities, Fréchet and Gateaux differentiability in optimization, weak sharp solution, minimum principle sufficiency property, Convexity of real functions of several variables, generalizations

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Access URL: https://zbmath.org/7345572
https://doi.org/10.1007/s11117-020-00765-7
https://link.springer.com/article/10.1007/s11117-020-00765-7

On weak sharp solutions in $(\rho , \mathbf{b}, \mathbf{d})$-variational inequalities: On weak sharp solutions in \((\rho , \mathbf{b}, \mathbf{d})\)-variational inequalities

Authors: Savin Treanţă

Source: Journal of Inequalities and Applications, Vol 2020, Iss 1, Pp 1-13 (2020)

Subject Terms: weak sharp solutions, Variational-type inequality, ( ρ , b , d ) $(\rho , \mathbf{b}, \mathbf{d})$ -convex path-independent curvilinear integral functional, QA1-939, 0211 other engineering and technologies, \((\rho,\mathbf{b},\mathbf{d})\)-convex path-independent curvilinear integral functional, 02 engineering and technology, Variational inequalities, variational-type inequality, Fréchet and Gateaux differentiability in optimization, Weak sharp solutions, Mathematics, Convexity of real functions of several variables, generalizations

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Access URL: https://zbmath.org/7460829
https://doi.org/10.1186/s13660-020-02323-x
https://doaj.org/article/cda9ff115709428790fa868fad3d038a
https://link.springer.com/content/pdf/10.1186/s13660-020-02323-x.pdf
https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-020-02323-x
https://link.springer.com/article/10.1186/s13660-020-02323-x

On Second-Order Generalized Convexity: On second-order generalized convexity

Authors: Constantin Zălinescu

Source: Journal of Optimization Theory and Applications. 168:802-829

Subject Terms: semidefinite matrix, 0101 mathematics, second-order convex function, 16. Peace & justice, Nonconvex programming, global optimization, 01 natural sciences, generalized convex functions, Convexity of real functions of several variables, generalizations, quadratic function

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Access URL: https://link.springer.com/10.1007/s10957-015-0820-y
https://dblp.uni-trier.de/db/journals/jota/jota168.html#Zalinescu16
https://link.springer.com/article/10.1007/s10957-015-0820-y

Hermite-Hadamard's inequalities for multivariate g-convex functions: Hermite-Hadamard's inequalities for multivariate \(g\)-convex functions

Authors: Josip Pečarić, M. Klaričić Bakula, Vida Šimić, Edward Neuman

Contributors: Uglešić, Nikica

Source: Mathematical Inequalities & Applications. :305-316

Subject Terms: r-convexity, multivariate g-convex functions, Hermite-Hadamardove nejednakosti, g-konveksne funkcije više varijabli, Hermite-Hadamard inequalities, \(g\)-convexity, 01 natural sciences, functional Stolarsky means, \(r\)-convexity, g-convexity, log-convexity, Inequalities for sums, series and integrals, logarithmic mean, 0101 mathematics, Hermite-Hadamard's inequalities, Convexity of real functions of several variables, generalizations, Means

File Description: application/xml

Access URL: http://files.ele-math.com/abstracts/mia-08-28-abs.pdf
https://www.bib.irb.hr/201091
https://www.bib.irb.hr/196216
https://zbmath.org/2212036
https://doi.org/10.7153/mia-08-28
https://files.ele-math.com/articles/mia-08-28.pdf
https://doi.org/10.7153/mia-08-28
http://files.ele-math.com/abstracts/mia-08-28-abs.pdf
http://mia.ele-math.com/08-28

A sharp Blaschke–Santaló inequality for $$\alpha $$ α -concave functions: A sharp Blaschke-Santaló inequality for \(\alpha \)-concave functions

Authors: Liran Rotem

Source: Geometriae Dedicata. 172:217-228

Subject Terms: \(\alpha\)-concavity, Inequalities and extremum problems involving convexity in convex geometry, polarity, log-concavity, 0101 mathematics, 16. Peace & justice, 01 natural sciences, Convexity of real functions of several variables, generalizations, Blaschke-Santaló inequality

File Description: application/xml

Access URL: https://zbmath.org/6358008
https://doi.org/10.1007/s10711-013-9917-3
https://link.springer.com/article/10.1007/s10711-013-9917-3
https://link.springer.com/article/10.1007/s10711-013-9917-3/fulltext.html
https://experts.umn.edu/en/publications/a-sharp-blaschkesantal%C3%B3-inequality-for-%CE%B1-concave-functions

Relaxation of certain integral functionals depending on strain and chemical composition

Authors: Ana Margarida Ribeiro, ZAPPALE, ELVIRA

Source: Chinese Annals of Mathematics, Series B. 34:491-514

Subject Terms: quasiconvexity, Mathematics - Analysis of PDEs, relaxation, Methods involving semicontinuity and convergence, functions of bounded variation, Coupling of solid mechanics with other effects, FOS: Mathematics, Relaxation, Convexity of real functions of several variables, generalizations, Absolutely continuous real functions of several variables, functions of bounded variation, Analysis of PDEs (math.AP)

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/pdf/1211.2574
http://arxiv.org/abs/1211.2574
https://www.iris.unisa.it/handle/11386/3878695
https://link.springer.com/article/10.1007/s11401-013-0784-x
https://hdl.handle.net/11386/3878695
https://doi.org/10.1007/s11401-013-0784-x

Quasiconvex functions and null Lagrangians in the stability problems of classes of mappings

Authors: A. A. Egorov

Source: Siberian Mathematical Journal. 49:637-649

Subject Terms: Variational methods applied to PDEs, stability of classes of mappings, Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations, Nonlinear first-order PDEs, 0102 computer and information sciences, quasiconvex function, 0101 mathematics, 01 natural sciences, Convexity of real functions of several variables, generalizations, null Lagrangian

File Description: application/xml

Access URL: https://zbmath.org/5381090
https://eudml.org/doc/55647
https://link.springer.com/article/10.1007/s11202-008-0060-6

Generalized convexities and generalized gradients based on algebraic operations

Authors: Department of Mathematics, Hanshan Teacher College, Chaozhou, Guangdong Province 521041, China ( host institution ), Yuan, Dehui, Chinchuluun, Altannar, Liu, Xiaoling, Pardalos, Panos M.

Source: Journal of Mathematical Analysis and Applications. 321:675-690

Subject Terms: generalized convexity, ( φ, Generalized convexity, Convex programming, (\(\phi\), \(\gamma\))-subdifferential, (φ,γ)-Convexity, Applied Mathematics, Generalized monotonicity, Nonsmooth analysis, 0211 other engineering and technologies, (φ,γ)-Subdifferential, 02 engineering and technology, 01 natural sciences, generalized monotonicity, γ ) -Convexity, γ ) -Subdifferential, \((\phi, \gamma)\)-convexity, Optimality conditions and duality in mathematical programming, 0101 mathematics, Analysis, Convexity of real functions of several variables, generalizations

File Description: application/xml; [Elsevier APIv3]

Access URL: https://ui.adsabs.harvard.edu/abs/2006JMAA..321..675Y/abstract
https://www.sciencedirect.com/science/article/pii/S0022247X0500884X
https://core.ac.uk/display/82688287
https://www.sciencedirect.com/science/article/abs/pii/S0022247X0500884X

Discrete Convexity: Discrete convexity

Authors: Danilov, V. I., Koshevoj, G. A.

Source: Journal of Mathematical Sciences. 133:1418-1421

Subject Terms: polymatroidal discretely concave functions, Convex functions and convex programs in convex geometry, Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry), separation theorem, Convexity of real functions of several variables, generalizations

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