Convex functions and the hadamard inequality

The Hadamard inequality is proven without resorting to any properties of the derivative. Only the convexity of the function in a closed interval is needed. Furthermore, if the existence of the integral is assumed, then the convexity requirement is weakened to convexity in the sense of Jensen. Both t...

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Autores:
Azpeitia, Alfonso G.
Tipo de recurso:
Article of journal
Fecha de publicación:
1994
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/43486
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/43486
http://bdigital.unal.edu.co/33584/
Palabra clave:
Convex and concave functions
arithmetic means
convexity inequalities
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Azpeitia, Alfonso G.61e20902-3080-4cc1-8a38-691fdccf239c3002019-06-28T12:02:28Z2019-06-28T12:02:28Z1994https://repositorio.unal.edu.co/handle/unal/43486http://bdigital.unal.edu.co/33584/The Hadamard inequality is proven without resorting to any properties of the derivative. Only the convexity of the function in a closed interval is needed. Furthermore, if the existence of the integral is assumed, then the convexity requirement is weakened to convexity in the sense of Jensen. Both the Hadamard inequality and a corresponding upper bound are generalized for integrals of the Stieljes type.application/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/33459Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 28, núm. 1 (1994); 7-12 0034-7426Azpeitia, Alfonso G. (1994) Convex functions and the hadamard inequality. Revista Colombiana de Matemáticas; Vol. 28, núm. 1 (1994); 7-12 0034-7426 .Convex functions and the hadamard inequalityArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTConvex and concave functionsarithmetic meansconvexity inequalitiesORIGINAL33459-124117-1-PB.pdfapplication/pdf1591315https://repositorio.unal.edu.co/bitstream/unal/43486/1/33459-124117-1-PB.pdfcee4750ef3135bbdcabb6b7060d1dea4MD51THUMBNAIL33459-124117-1-PB.pdf.jpg33459-124117-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg5584https://repositorio.unal.edu.co/bitstream/unal/43486/2/33459-124117-1-PB.pdf.jpg17dd398a7d1fb6dcbcfff5d46a36559dMD52unal/43486oai:repositorio.unal.edu.co:unal/434862024-02-10 23:06:22.532Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Convex functions and the hadamard inequality
title Convex functions and the hadamard inequality
spellingShingle Convex functions and the hadamard inequality
Convex and concave functions
arithmetic means
convexity inequalities
title_short Convex functions and the hadamard inequality
title_full Convex functions and the hadamard inequality
title_fullStr Convex functions and the hadamard inequality
title_full_unstemmed Convex functions and the hadamard inequality
title_sort Convex functions and the hadamard inequality
dc.creator.fl_str_mv Azpeitia, Alfonso G.
dc.contributor.author.spa.fl_str_mv Azpeitia, Alfonso G.
dc.subject.proposal.spa.fl_str_mv Convex and concave functions
arithmetic means
convexity inequalities
topic Convex and concave functions
arithmetic means
convexity inequalities
description The Hadamard inequality is proven without resorting to any properties of the derivative. Only the convexity of the function in a closed interval is needed. Furthermore, if the existence of the integral is assumed, then the convexity requirement is weakened to convexity in the sense of Jensen. Both the Hadamard inequality and a corresponding upper bound are generalized for integrals of the Stieljes type.
publishDate 1994
dc.date.issued.spa.fl_str_mv 1994
dc.date.accessioned.spa.fl_str_mv 2019-06-28T12:02:28Z
dc.date.available.spa.fl_str_mv 2019-06-28T12:02:28Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/43486
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url https://repositorio.unal.edu.co/handle/unal/43486
http://bdigital.unal.edu.co/33584/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv http://revistas.unal.edu.co/index.php/recolma/article/view/33459
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas
Revista Colombiana de Matemáticas
dc.relation.ispartofseries.none.fl_str_mv Revista Colombiana de Matemáticas; Vol. 28, núm. 1 (1994); 7-12 0034-7426
dc.relation.references.spa.fl_str_mv Azpeitia, Alfonso G. (1994) Convex functions and the hadamard inequality. Revista Colombiana de Matemáticas; Vol. 28, núm. 1 (1994); 7-12 0034-7426 .
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
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dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas
institution Universidad Nacional de Colombia
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repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
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