Some improvements of McShane and Hölder-type inequalities via superquadratic functions

Authors: Shumaila Rani, Rabia Bibi

Source: Journal of Inequalities and Applications, Vol 2024, Iss 1, Pp 1-13 (2024)

Subject Terms: superquadratic functions, Time-scale calculus, Hölder's inequality, 01 natural sciences, Superquadratic functions, Dynamic equations on time scales or measure chains, McShane's inequality, time-scale calculus, QA1-939, Inequalities for sums, series and integrals, positive linear functionals, Positive linear functionals, 0101 mathematics, Integration with respect to measures and other set functions, Mathematics

File Description: application/xml

Access URL: https://doaj.org/article/4a9ac2d569884f28882e676d093df4a5

Coarea inequality for monotone functions on metric surfaces

Authors: Ikonen, Toni, Rajala, Kai, Esmayli, Behnam

Source: Transactions of the American Mathematical Society.

Subject Terms: Length, area, volume, other geometric measure theory, ta111, Metric Geometry (math.MG), Inequalities in metric spaces, metriset avaruudet, 01 natural sciences, integraaliyhtälöt, Hausdorff and packing measures, Mathematics - Metric Geometry, 28A25, 28A75, 28A78, 30L10, 30L15, Quasiconformal mappings in metric spaces, FOS: Mathematics, Matematiikka, mittateoria, 0101 mathematics, epäyhtälöt, Integration with respect to measures and other set functions, Mathematics

File Description: application/xml; application/pdf; fulltext

Access URL: http://arxiv.org/abs/2208.06185
http://juuli.fi/Record/0677160623
https://doi.org/10.1090/tran/8998
http://urn.fi/URN:NBN:fi:jyu-202402222061

Perturbed Evolution Problems with Continuous Bounded Variation in Time and Applications: Perturbed evolution problems with continuous bounded variation in time and applications

Authors: Dalila Azzam-Laouir, Charles Castaing, M. D. P. Monteiro Marques

Source: Set-Valued and Variational Analysis. 26:693-728

Subject Terms: Functional-differential inclusions, pseudo-distance, Skorokhod problem, Evolution inclusions, perturbation, 0211 other engineering and technologies, 02 engineering and technology, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, maximal monotone operator, 01 natural sciences, control theory, Stochastic ordinary differential equations (aspects of stochastic analysis), Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.), bounded variation, Lipschitz, 0101 mathematics, Integration with respect to measures and other set functions, Ordinary differential inclusions, Control problems involving ordinary differential equations, existence and uniqueness

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Access URL: https://zbmath.org/6936449
https://doi.org/10.1007/s11228-017-0432-9
https://link.springer.com/article/10.1007/s11228-017-0432-9

A measure theoretic perspective on the space of Feynman diagrams

Authors: Ali Shojaei-Fard

Source: Boletín de la Sociedad Matemática Mexicana. 24:507-533

Subject Terms: measure theory, Infinite graphs, 0103 physical sciences, Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc, operational calculus, 0101 mathematics, Integration with respect to measures and other set functions, Green's functions for elliptic equations, quantum field theory, 01 natural sciences, Feynman diagrams, graphons, Nonperturbative methods of renormalization applied to problems in quantum field theory

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/s40590-017-0166-6
https://dialnet.unirioja.es/servlet/articulo?codigo=6767195

The (sub/super)additivity assertion of Choquet

Authors: Heinz König

Source: Measure and Integration ISBN: 9783034803816

Subject Terms: convex functions, Riesz representation, Measures and integration on abstract linear spaces, (sub/super)modular functionals, 02 engineering and technology, Set functions and measures on topological spaces (regularity of measures, etc.), Stonean function classes, 01 natural sciences, Stonean and truncable functionals, (sub/super)additive functionals, Danull-Stone representation, Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures, 0202 electrical engineering, electronic engineering, information engineering, Choquet integral, Contents, measures, outer measures, capacities, 0101 mathematics, Integration with respect to measures and other set functions

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Access URL: https://www.impan.pl/shop/publication/transaction/download/product/89574?download.pdf
http://www.math.uni-sb.de/service/preprints/preprint84.pdf
https://zbmath.org/1927670
https://doi.org/10.4064/sm157-2-4
https://www.impan.pl/en/publishing-house/journals-and-series/studia-mathematica/all/157/2/89574/the-sub-super-additivity-assertion-of-choquet
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-sm157-2-4
http://journals.impan.pl/cgi-bin/doi?sm157-2-4
https://publikationen.sulb.uni-saarland.de/handle/20.500.11880/26292
https://rd.springer.com/chapter/10.1007/978-3-0348-0382-3_12
https://publikationen.sulb.uni-saarland.de/bitstream/20.500.11880/26292/1/preprint_84_03.pdf

On the inner Daniell-Stone and Riesz representation theorems

Authors: Heinz König

Source: Measure and Integration ISBN: 9783034803816

Subject Terms: theorem of Kisyński, inner premeasures, Radon premeasures, Set functions and measures on topological spaces (regularity of measures, etc.), inner preintegrals, tightness, inner extension, 01 natural sciences, inner sources, inner extensions, Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures, positive (isotone) linear functionals, Radon measures, Contents, measures, outer measures, capacities, 0101 mathematics, Integration with respect to measures and other set functions, Radon preintegrals

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Access URL: https://zbmath.org/1477084
https://publikationen.sulb.uni-saarland.de/bitstream/20.500.11880/26226/1/preprint_12_00.pdf
https://rd.springer.com/chapter/10.1007/978-3-0348-0382-3_8
http://scidok.sulb.uni-saarland.de/volltexte/2011/4279/
https://link.springer.com/chapter/10.1007/978-3-0348-0382-3_8
https://publikationen.sulb.uni-saarland.de/handle/20.500.11880/26226
https://link.springer.com/content/pdf/10.1007%2F978-3-0348-0382-3_8.pdf

Measure and Integration: Comparison of old and new procedures: Measure and integration: Comparison of old and new procedures

Authors: Heinz König

Source: Measure and Integration ISBN: 9783034803816

Subject Terms: Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures, regularity, 9. Industry and infrastructure, 4. Education, 0103 physical sciences, Contents, measures, outer measures, capacities, outer and inner extension theories, 0101 mathematics, Set functions and measures on topological spaces (regularity of measures, etc.), 16. Peace & justice, Integration with respect to measures and other set functions, 01 natural sciences, Daniell-Stone theorem

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Access URL: https://zbmath.org/1295491
https://rd.springer.com/chapter/10.1007/978-3-0348-0382-3_5
https://link.springer.com/article/10.1007/s000130050322
https://link.springer.com/content/pdf/10.1007%2F978-3-0348-0382-3_5.pdf

A numerical method for the Landau–Lifshitz equation with magnetostriction: A numerical method for the Landau-Lifshitz equation with magnetostriction

Authors: Banas, Lubomir

Source: Mathematical Methods in the Applied Sciences. 28:1939-1954

Subject Terms: Variational methods applied to problems in optics and electromagnetic theory, Statistical mechanics of magnetic materials, Landau-Lifshitz equation, numerical methods, 0101 mathematics, magnetostriction, Integration with respect to measures and other set functions, 01 natural sciences

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Access URL: https://zbmath.org/2236549
https://doi.org/10.1002/mma.651
https://ui.adsabs.harvard.edu/abs/2005MMAS...28.1939B/abstract
https://onlinelibrary.wiley.com/doi/10.1002/mma.651

Rearrangement Inequalities with Application to Ratios of Heat Kernels: Rearrangement inequalities with application to ratios of heat kernels

Authors: Cristina Draghici

Source: Potential Analysis. 22:351-374

Subject Terms: symmetrization, Schrödinger operator, Schrödinger equation, rearrangement, integral inequality, Inequalities for sums, series and integrals, 0101 mathematics, Integration with respect to measures and other set functions, heat kernels, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007%2Fs11118-004-1328-5

A characterisation of multipliers for the Henstock–Kurzweil integral: A characterisation of multipliers for the Henstock-Kurzweil integral

Authors: Lee Tuo–Yeong

Source: Mathematical Proceedings of the Cambridge Philosophical Society. 138:487-492

Subject Terms: Henstock integral, Kurzweil integral, Functions of several variables, multiplier, Denjoy and Perron integrals, other special integrals, 0101 mathematics, Integration with respect to measures and other set functions, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/2177506
https://doi.org/10.1017/s030500410500839x
https://dialnet.unirioja.es/servlet/articulo?codigo=1174707
https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/characterisation-of-multipliers-for-the-henstockkurzweil-integral/5F28B6EBF06B0B2B56B3AD5FFE29B2E1
http://ui.adsabs.harvard.edu/abs/2005MPCPS.138..487T/abstract
http://www.journals.cambridge.org/abstract_S030500410500839X

What is known about unit cubes

Authors: Chuanming Zong

Source: Bulletin of the American Mathematical Society. 42:181-212

Subject Terms: Finite abelian groups, projections, Matrices over special rings (quaternions, finite fields, etc.), Exact enumeration problems, generating functions, triangulations, cross sections, \(0/1\) polytopes Minkowski conjecture, Tilings in \(2\) dimensions (aspects of discrete geometry), 01 natural sciences, Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.), Lattice packing and covering (number-theoretic aspects), Simultaneous homogeneous approximation, linear forms, Combinatorial aspects of tessellation and tiling problems, Tilings in \(n\) dimensions (aspects of discrete geometry), Combinatorial aspects of finite geometries, inscribed simplex, Keller conjecture, 0101 mathematics, Integration with respect to measures and other set functions, Combinatorial aspects of matrices (incidence, Hadamard, etc.)

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Access URL: https://www.ams.org/bull/2005-42-02/S0273-0979-05-01050-5/S0273-0979-05-01050-5.pdf
https://zbmath.org/2150886
https://doi.org/10.1090/s0273-0979-05-01050-5
http://math.uchicago.edu/~shmuel/AAT-readings/Combinatorial%20Geometry
%20Concentration
%20Real%20Algebraic%20Geometry/Zong
%20unit%20cubes.pdf
https://www.ams.org/journals/bull/2005-42-02/S0273-0979-05-01050-5/home.html
https://www.ams.org/bull/2005-42-02/S0273-0979-05-01050-5/S0273-0979-05-01050-5.pdf
https://doi.org/10.1090%2FS0273-0979-05-01050-5

Domains, integration and ‘positive analysis’: Domains, integration and `positive analysis'

Authors: Jimmie Lawson

Source: Mathematical Structures in Computer Science. 14:815-832

Subject Terms: Other connections with logic and set theory, S-integral, 0102 computer and information sciences, Riemann-Edalat integral, 01 natural sciences, Continuous lattices and posets, applications, continuous domain, survey, Contents, measures, outer measures, capacities, horizontal integral, 0101 mathematics, Integration with respect to measures and other set functions, valuation, Constructive real analysis, Constructive and recursive analysis

File Description: application/xml

Access URL: https://zbmath.org/2147881
https://doi.org/10.1017/s0960129504004372
https://digitalcommons.lsu.edu/mathematics_pubs/623/
https://dblp.uni-trier.de/db/journals/mscs/mscs14.html#Lawson04
http://dblp.uni-trier.de/db/journals/mscs/mscs14.html#Lawson04
https://dialnet.unirioja.es/servlet/articulo?codigo=1053897
http://journals.cambridge.org/abstract_S0960129504004372
https://www.cambridge.org/core/journals/mathematical-structures-in-computer-science/article/domains-integration-and-positive-analysis/973D2767FC698A51EFD5A6C4C27403AA

A general rearrangement inequality

Authors: Cristina Draghici

Source: Proceedings of the American Mathematical Society. 133:735-743

Subject Terms: symmetrization, rearrangement, integral inequality, Inequalities for sums, series and integrals, 0101 mathematics, Integration with respect to measures and other set functions, 01 natural sciences

File Description: application/xml

Access URL: https://www.ams.org/proc/2005-133-03/S0002-9939-04-07729-9/S0002-9939-04-07729-9.pdf
https://zbmath.org/2120780
https://doi.org/10.1090/s0002-9939-04-07729-9
https://dialnet.unirioja.es/servlet/articulo?codigo=1119845
https://www.ams.org/proc/2005-133-03/S0002-9939-04-07729-9/S0002-9939-04-07729-9.pdf
https://documat.unirioja.es/servlet/articulo?codigo=1119845
https://www.ams.org/journals/proc/2005-133-03/S0002-9939-04-07729-9/

On the Measurability of Functions with Respect to Certain Classes of Measures: On the measurability of functions with respect to certain classes of measures

Authors: Alexander Kharazishvili, A. Kirtadze

Source: gmj. 11:489-494

Subject Terms: Vitali partition, absolutely nonmeasurable function, Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets, Contents, measures, outer measures, capacities, 0101 mathematics, Measure-preserving transformations, extension of measure, Integration with respect to measures and other set functions, generalized Luzin set, 01 natural sciences

File Description: application/xml

Access URL: http://www.heldermann-verlag.de/gmj/gmj11/gmj11042.pdf
https://zbmath.org/2114273
https://www.degruyter.com/dg/viewarticle.layout.displayshoppingcartlink:shoppingcartinfolink?format=INT&t:ac=j$002fgmj.2004.11.issue-3$002fgmj.2004.489$002fgmj.2004.489.xml
http://www.heldermann-verlag.de/gmj/gmj11/gmj11042.pdf

Riemann and Edalat integration on domains: Riemann and Edalat integration on domains.

Authors: Jimmie Lawson, Bin Lu

Source: Theoretical Computer Science. 305:259-275

Subject Terms: domain theory, Continuous domain, Theory of computing, 0102 computer and information sciences, Integrals of Riemann, Stieltjes and Lebesgue type, Algebra of sets, 01 natural sciences, Valuation, Theoretical Computer Science, Riemann integral, Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures, continuous domain, Finitely additive measure, algebra of sets, Contents, measures, outer measures, capacities, 0101 mathematics, Integration with respect to measures and other set functions, valuation, finitely additive measure, Computer Science(all)

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Access URL: https://zbmath.org/2055976
https://doi.org/10.1016/s0304-3975(02)00696-5
https://dblp.uni-trier.de/db/journals/tcs/tcs305.html#LawsonL03
https://www.sciencedirect.com/science/article/pii/S0304397502006965
https://digitalcommons.lsu.edu/mathematics_pubs/624/
http://www.sciencedirect.com/science/article/pii/S0304397502006965

Integrals and derivatives on net fractals: Integrals and derivatives on net fractals.

Authors: Xiao-Tian Wang, Jin-Rong Liang, Fu-Yao Ren, Wei-Yuan Qiu

Source: Chaos, Solitons & Fractals. 16:107-117

Subject Terms: Fractals, calculus on net fractals, 0103 physical sciences, derivatives, net fractals, Integrals, Integration with respect to measures and other set functions, 01 natural sciences, net measures

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/S0960077902002114
https://ui.adsabs.harvard.edu/abs/2003CSF....16..107R/abstract

Representability of Analytic Functions in Terms of Their Boundary Values: Representability of analytic functions in terms of their boundary values

Authors: Rashid A. Aliev

Source: Mathematical Notes. 73:8-20

Subject Terms: complex Borel measure, Hölder continuity, Lebesgue measure, Cauchy integral, 0103 physical sciences, Integral representations, integral operators, integral equations methods in two dimensions, 0101 mathematics, Poisson integral, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, Integration with respect to measures and other set functions, 01 natural sciences, analytic function

File Description: application/xml

Access URL: https://zbmath.org/1928357
https://doi.org/10.1023/a:1022113831759
https://link.springer.com/article/10.1023/A:1022113831759

representability of analytic functions in terms of their boundary values: Representability of analytic functions in terms of their boundary values

Authors: Rashid A. Aliev

Source: Mathematical Notes. 73(1):8-20

Subject Terms: complex Borel measure, Hölder continuity, Lebesgue measure, Cauchy integral, Integral representations, integral operators, integral equations methods in two dimensions, Poisson integral, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, Integration with respect to measures and other set functions, analytic function

File Description: application/xml

Access URL: https://zbmath.org/1928357
https://doi.org/10.1023/a:1022113831759
https://link.springer.com/article/10.1023/A:1022113831759

Lower semicontinuity of multiple µ-quasiconvex integrals: Lower semicontinuity of multiple \(\mu\)-quasiconvex integrals.

Authors: Ilaria Fragalà

Source: ESAIM: Control, Optimisation and Calculus of Variations. 9:105-124

Subject Terms: tangent properties, lower semicontinuity, Methods involving semicontinuity and convergence, relaxation, Borel measures, Existence theories for free problems in two or more independent variables, 0101 mathematics, Integration with respect to measures and other set functions, 01 natural sciences

File Description: application/xml

Access URL: https://www.esaim-cocv.org/articles/cocv/pdf/2003/01/cocv259.pdf
http://www.esaim-cocv.org/articles/cocv/pdf/2003/01/cocv259.pdf
http://www.numdam.org/item/10.1051/cocv:2003002.pdf
http://www.numdam.org/articles/10.1051/cocv:2003002/
https://eudml.org/doc/90683
https://www.esaim-cocv.org/articles/cocv/abs/2003/01/cocv259/cocv259.html
http://www.numdam.org/item?id=COCV_2003__9__105_0

EXPONENTIAL INTEGRABILITY FOR IMAGES OF ORNSTEIN–UHLENBECK OPERATORS ACTING ON CYLINDER FUNCTIONS ON LOOP SPACES: Exponential integrability for images of Ornstein-Uhlenbeck operators acting on cylinder functions on loop spaces

Authors: Fuzhou Gong

Source: Infinite Dimensional Analysis, Quantum Probability and Related Topics. :541-553

Subject Terms: Diffusion processes and stochastic analysis on manifolds, exponential integrability, loop spaces, Brownian motion, 0101 mathematics, Integration with respect to measures and other set functions, 01 natural sciences, Ornstein-Uhlenbeck operators

File Description: application/xml

Access URL: https://zbmath.org/2102822
https://doi.org/10.1142/s0219025702000961
https://www.worldscientific.com/doi/pdf/10.1142/S0219025702000961