Search Results - Calculus of functions taking values in infinite-dimensional spaces*

The Banach-Zarecki theorem for functions with values in metric spaces

Authors: Luděk Zajíček Jakub Duda

Source: Proceedings of the American Mathematical Society. 133:3631-3633

Subject Terms: Lusin (N) condition, Calculus of functions taking values in infinite-dimensional spaces, Banach-Zarecki theorem, absolute continuity, Absolutely continuous real functions in one variable, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://www.ams.org/proc/2005-133-12/S0002-9939-05-07959-1/S0002-9939-05-07959-1.pdf
https://dialnet.unirioja.es/servlet/articulo?codigo=1377323
https://www.ams.org/journals/proc/2005-133-12/S0002-9939-05-07959-1/home.html

Flett′s mean value theorem in topological vector spaces: Flett's mean value theorem in topological vector spaces

Authors: Thomas Riedel Prasanna K. Sahoo Robert C. Powers

Source: International Journal of Mathematics and Mathematical Sciences, Vol 27, Iss 11, Pp 689-694 (2001)

Subject Terms: Calculus of functions taking values in infinite-dimensional spaces, Derivatives of functions in infinite-dimensional spaces, QA1-939, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, Gâteaux differentiable functions, 0101 mathematics, 01 natural sciences, Mathematics

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Access URL: http://downloads.hindawi.com/journals/ijmms/2001/894240.pdf
https://zbmath.org/1716633
https://doi.org/10.1155/s016117120101078x
https://doaj.org/article/e6f81bd06e094cf7a0913d039ac97858
https://www.hindawi.com/journals/ijmms/2001/894240/reprint/
https://downloads.hindawi.com/journals/ijmms/2001/894240.pdf
https://www.hindawi.com/journals/ijmms/2001/894240/
http://downloads.hindawi.com/journals/ijmms/2001/894240.pdf

Differential calculus over general base fields and rings: Differential calculus over general base fields and rings.

Authors: Karl-Hermann Neeb Wolfgang Bertram Helge Glöckner

Source: Expositiones Mathematicae. 22:213-282

Subject Terms: non-archimedian analysis, Mathematics(all), Calculus of functions on infinite-dimensional spaces, Calculus of functions taking values in infinite-dimensional spaces, Infinite-dimensional Lie groups and their Lie algebras: general properties, infinite-dimensional Lie groups, topological fields, polynomial maps, rational manifolds, 01 natural sciences, non-archimedean analysis, differential calculus, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, Non-Archimedean analysis, 0101 mathematics, infinite-dimensional manifolds

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Access URL: https://zbmath.org/2222515
https://doi.org/10.1016/s0723-0869(04)80006-9
https://www.sciencedirect.com/science/article/abs/pii/S0723086904800069
http://tubiblio.ulb.tu-darmstadt.de/8352/
https://hal.archives-ouvertes.fr/hal-00141431
https://www.sciencedirect.com/science/article/pii/S0723086904800069

Hölder continuous homomorphisms between infinite-dimensional Lie groups are smooth

Authors: Helge Glöckner

Source: Journal of Functional Analysis. 228:419-444

Subject Terms: Calculus of functions on infinite-dimensional spaces, Differentiability, Infinite-dimensional Lie group, Group Theory (math.GR), 01 natural sciences, Continuous and differentiable maps in nonlinear functional analysis, 22E65 (Primary) 26E15, 26E20, 26E30, 46T20, 58C20 (Secondary), Power map, FOS: Mathematics, 0101 mathematics, Calculus of functions taking values in infinite-dimensional spaces, Hölder continuity, Taylor expansion, Infinite-dimensional Lie groups and their Lie algebras: general properties, Lipschitz continuity, Smoothness, Functional Analysis (math.FA), Mathematics - Functional Analysis, Analysis on \(p\)-adic Lie groups, Homomorphism, Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions, non-Archimedean functional analysis, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, Non-Archimedean analysis, Mathematics - Group Theory, infinite-dimensional Lie group, Analysis, differentiability

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Access URL: http://arxiv.org/abs/math/0403251
https://www.sciencedirect.com/science/article/pii/S0022123605002892
https://core.ac.uk/display/82696344

Duality in the space of regulated functions and the play operator

Authors: Martin Brokate Pavel Krejčí

Source: Mathematische Zeitschrift. 245:667-688

Subject Terms: Spaces of vector- and operator-valued functions, Calculus of functions taking values in infinite-dimensional spaces, Functions of bounded variation, generalizations, Denjoy and Perron integrals, other special integrals, 0101 mathematics, regulated functions, functions with bounded variation, 01 natural sciences, Hysteresis for ordinary differential equations

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Access URL: https://link.springer.com/article/10.1007/s00209-003-0563-6
https://documat.unirioja.es/servlet/articulo?codigo=2806754
https://dialnet.unirioja.es/servlet/articulo?codigo=2806668

A characterization of quasiconvex vector-valued functions

Authors: Benoist, Joël Borwein, Jonathan M. Popovici, Nicolae et al.

Contributors: Benoist, Joël Borwein, Jonathan M. Popovici, Nicolae et al.

Source: Proceedings of the American Mathematical Society. 131:1109-1113

Subject Terms: scalarization, Banach space, Calculus of functions taking values in infinite-dimensional spaces, 0211 other engineering and technologies, 02 engineering and technology, 01 natural sciences, vector-valued functions, quasiconvexity, polar cones, 0101 mathematics, quasiconvex vector-valued functions, Multi-objective and goal programming, Convexity of real functions of several variables, generalizations

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Access URL: https://www.ams.org/proc/2003-131-04/S0002-9939-02-06761-8/S0002-9939-02-06761-8.pdf
https://zbmath.org/1849931
https://doi.org/10.1090/s0002-9939-02-06761-8
http://docserver.carma.newcastle.edu.au/145/
https://dialnet.unirioja.es/servlet/articulo?codigo=321468
https://www.unilim.fr/pages_perso/joel.benoist/articles/bebopo.pdf
https://www.jstor.org/stable/1194189
https://www.ams.org/journals/proc/2003-131-04/S0002-9939-02-06761-8/home.html
https://www.ams.org/proc/2003-131-04/S0002-9939-02-06761-8/S0002-9939-02-06761-8.pdf

Functions of class $C^k$ without derivatives: Functions of class \(C^k\) without derivatives

Authors: Tuynman, G. M.

Source: Recercat. Dipósit de la Recerca de Catalunya
instname
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Publicacions Matemàtiques; Vol. 41, Núm. 2 (1997); p. 417-435

Subject Terms: topological abelian groups, Calculus of functions taking values in infinite-dimensional spaces, linearizing factor, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, functions of class \(C^k\), Fréchet and Gateaux differentiability in optimization

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Access URL: https://ddd.uab.cat/pub/pubmat/02141493v41n2/02141493v41n2p417.pdf
http://hdl.handle.net/2072/381566
https://ddd.uab.cat/record/13067
http://mat.uab.cat/pubmat/articles/view_doi/10.5565/PUBLMAT_41297_08
https://dialnet.unirioja.es/servlet/articulo?codigo=2137503
https://ddd.uab.cat/pub/pubmat/02141493v41n2/02141493v41n2p417.pdf
http://www.raco.cat/index.php/PublicacionsMatematiques/article/view/37904

A chain rule for nonsmooth composite functions via minimisation

Authors: D. Ralph

Source: Bulletin of the Australian Mathematical Society. 49:129-137

Subject Terms: Programming in abstract spaces, composition of nonsmooth vector valued and real valued functions, Calculus of functions taking values in infinite-dimensional spaces, generalized gradient, Nonsmooth analysis, 0211 other engineering and technologies, chain rule, 02 engineering and technology, 0101 mathematics, 01 natural sciences

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Access URL: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/68E9C5FD09AC37C7B2E5BB5C930C15E1/S0004972700016178a.pdf/div-class-title-a-chain-rule-for-nonsmooth-composite-functions-via-minimisation-div.pdf
https://zbmath.org/563225
https://doi.org/10.1017/s0004972700016178
http://www.journals.cambridge.org/abstract_S0004972700016178

Locally compactly Lipschitzian mappings in infinite dimensional programming

Authors: B.M. Glover

Source: Bulletin of the Australian Mathematical Society. 47:395-406

Subject Terms: Programming in abstract spaces, Calculus of functions taking values in infinite-dimensional spaces, locally compactly Lipschitzian mapping, subgradient multifunction, Nonsmooth analysis, 0211 other engineering and technologies, 02 engineering and technology

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Access URL: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C8DE11545A91F04098484CEE19CE7055/S0004972700015227a.pdf/div-class-title-locally-compactly-lipschitzian-mappings-in-infinite-dimensional-programming-div.pdf
https://zbmath.org/427722
https://doi.org/10.1017/s0004972700015227
http://www.journals.cambridge.org/abstract_S0004972700015227
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0004972700015227

Monotone and convex H*‐algebra valued functions: Monotone and convex \(H^*\)-algebra valued functions

Authors: Parfeny P. Saworotnow

Source: International Journal of Mathematics and Mathematical Sciences, Vol 19, Iss 3, Pp 473-479 (1996)

Subject Terms: convex function, convex functions, monotone functions, Calculus of functions taking values in infinite-dimensional spaces, Stieltjes integral, Banach *-algebra, saltus function, Integrals of Riemann, Stieltjes and Lebesgue type, 01 natural sciences, Monotonic functions, generalizations, Convexity of real functions in one variable, generalizations, Hilbert algebras, H*-algebra, trace-class, Hilbert Schmidt operators, QA1-939, \(H^*\)-algebra, Borel measure, Vector-valued measures and integration, 0101 mathematics, Mathematics

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Access URL: http://downloads.hindawi.com/journals/ijmms/1996/726464.pdf
https://doaj.org/article/b88a4145ecef4a7f871046fabd3239e6
https://www.hindawi.com/journals/ijmms/1996/726464/
https://downloads.hindawi.com/journals/ijmms/1996/726464.pdf

Representation of Integral Formulas for the Extended Quaternions on Clifford Analysis.

Authors: Kim, Ji Eun

Source: Mathematics (2227-7390); Sep2025, Vol. 13 Issue 17, p2730, 18p

Subject Terms: INTEGRAL representations, QUATERNIONS, INTEGRALS, QUATERNION functions, CLIFFORD algebras, MATHEMATICAL physics, BOUNDARY value problems, PARTIAL differential equations

Conveniently Hölder Homomorphisms are Smooth in the Convenient Sense: Conveniently Hölder homomorphisms are smooth in the convenient sense

Authors: Helge Glöckner

Source: Annals of Global Analysis and Geometry. 27:227-255

Subject Terms: Calculus of functions on infinite-dimensional spaces, Calculus of functions taking values in infinite-dimensional spaces, Infinite-dimensional Lie groups and their Lie algebras: general properties, Group Theory (math.GR), 01 natural sciences, Hölder condition, Continuous and differentiable maps in nonlinear functional analysis, Lie group, 22E65 (Primary) 26E15, 26E20, 46T20, 58C20 (Secondary), Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, convenient differential calculus, FOS: Mathematics, 0101 mathematics, Mathematics - Group Theory

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Access URL: http://arxiv.org/pdf/math/0404344v1.pdf
http://arxiv.org/abs/math/0404344
https://link.springer.com/article/10.1007/s10455-005-0040-z

The Henstock integral for functions with values in nuclear spaces and the Henstock lemma

Authors: Nakanishi, Shizu

Subject Terms: Calculus of functions taking values in infinite-dimensional spaces, Henstock integral, Henstock's lemma, functions with values in nuclear spaces, Denjoy and Perron integrals, other special integrals, Vector-valued set functions, measures and integrals, Vector-valued measures and integration, countably Hilbert space

File Description: application/xml

Access URL: https://zbmath.org/1263683

On manifolds with non-negative Ricci curvature and Sobolev inequalities

Authors: Michel Ledoux

Source: Communications in Analysis and Geometry. 7:347-353

Subject Terms: Ricci curvature, Calculus of functions taking values in infinite-dimensional spaces, Riemann manifold, Sobolev inequality, compact support, 0101 mathematics, Integration on manifolds, measures on manifolds, 01 natural sciences, Global Riemannian geometry, including pinching

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Access URL: http://www.intlpress.com/site/pub/files/_fulltext/journals/cag/1999/0007/0002/CAG-1999-0007-0002-a007.pdf
https://www.intlpress.com/site/pub/files/_fulltext/journals/cag/1999/0007/0002/CAG-1999-0007-0002-a007.pdf
http://www.math.univ-toulouse.fr/~ledoux/Sobolev.pdf
https://intlpress.com/site/pub/pages/journals/items/cag/content/vols/0007/0002/a007/index.php

Toward an optimal theory of integration for functions taking values in quasi-Banach spaces.

Authors: Ansorena, José L. Bello, Glenier

Source: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales / RACSAM; Apr2022, Vol. 116 Issue 2, p1-27, 27p

Subdifferentials of nonconvex vector-valued functions

Authors: Lionel Thibault

Source: Journal of Mathematical Analysis and Applications. 86:319-344

Subject Terms: Calculus of functions taking values in infinite-dimensional spaces, Lattices of continuous, differentiable or analytic functions, Applied Mathematics, directional subderivative, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, 0211 other engineering and technologies, subdifferential, 02 engineering and technology, 0101 mathematics, 01 natural sciences, Analysis, tangent cone

File Description: application/xml

Access URL: https://zbmath.org/3774552
https://doi.org/10.1016/0022-247x(82)90226-8
https://www.sciencedirect.com/science/article/abs/pii/0022247X82902268
https://www.sciencedirect.com/science/article/pii/0022247X82902268

Convex programming on spaces of measurable functions

Authors: KOSHI, Shozo LAI, Hang Chin KOMURO, Naoto

Source: Hokkaido Math. J. 14, no. 1 (1985), 75-84

Subject Terms: Convex programming, conjugate functionals, Calculus of functions taking values in infinite-dimensional spaces, Duality theory for topological vector spaces, Methods involving semicontinuity and convergence, relaxation, Spaces of measures, convergence of measures, duality theorems, Fenchel-Moreau theorem, Duality theory (optimization), Spaces of measures, Convexity of real functions in one variable, generalizations, Ordered topological linear spaces, vector lattices

File Description: application/xml; application/pdf

Access URL: https://zbmath.org/3909183
https://doi.org/10.14492/hokmj/1381757690
https://projecteuclid.org/euclid.hokmj/1381757690
https://projecteuclid.org/download/pdf_1/euclid.hokmj/1381757690
http://projecteuclid.org/euclid.hokmj/1381757690

Functions of a real variable with values in a convergence vector space. I: Derivatives

Authors: Castañeda Bravo, F.

Subject Terms: Calculus of functions taking values in infinite-dimensional spaces, Derivatives of functions in infinite-dimensional spaces, function of one real variable with values in a space with convergence structure, n-th derivative

File Description: application/xml

Access URL: https://zbmath.org/3895324

Differential mean value properties for quasi-continuous functions

Authors: Turinici, Mihai

Subject Terms: Derivatives of functions in infinite-dimensional spaces, Calculus of functions taking values in infinite-dimensional spaces, Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems, exceptional set, oscillation value, quasi-continuous functions, Dini's numbers, equality mean value property, left derivative, nearly half-continuous vector functions, quasi-continuous real valued functions on locally convex spaces, linear variety, differential mean value, convex subsets and cones in locally convex spaces, convex hull, monotonicity principle, Ordered topological linear spaces, vector lattices

File Description: application/xml

Access URL: https://zbmath.org/1689538
https://zbmath.org/1644799
https://zbmath.org/1822157

Mean value theorem in topological vector spaces

Authors: Khan, Liaqat Ali

Subject Terms: General theory of locally convex spaces, Calculus of functions taking values in infinite-dimensional spaces, Hausdorff topological vector spaces, Gateaux differentiability, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems

File Description: application/xml

Access URL: https://zbmath.org/1102996