Improvements of Jensen-Type Inequalities for Diamond-α Integrals

We give further improvements of the Jensen inequality and its converse on time scales, allowing also negative weights. These results generalize the Jensen inequality and its converse for both discrete and continuous cases. Further, we investigate the exponential and logarithmic convexity of the diff...

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Detalles Bibliográficos
Autores principales: Bibi, Rabia, Pečarić, Josip, Lipanović, Mirna Rodić
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4897212/
https://www.ncbi.nlm.nih.gov/pubmed/27379320
http://dx.doi.org/10.1155/2014/580605
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author Bibi, Rabia
Pečarić, Josip
Lipanović, Mirna Rodić
author_facet Bibi, Rabia
Pečarić, Josip
Lipanović, Mirna Rodić
author_sort Bibi, Rabia
collection PubMed
description We give further improvements of the Jensen inequality and its converse on time scales, allowing also negative weights. These results generalize the Jensen inequality and its converse for both discrete and continuous cases. Further, we investigate the exponential and logarithmic convexity of the differences between the left-hand side and the right-hand side of these inequalities and present several families of functions for which these results can be applied.
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spelling pubmed-48972122016-07-04 Improvements of Jensen-Type Inequalities for Diamond-α Integrals Bibi, Rabia Pečarić, Josip Lipanović, Mirna Rodić Int Sch Res Notices Research Article We give further improvements of the Jensen inequality and its converse on time scales, allowing also negative weights. These results generalize the Jensen inequality and its converse for both discrete and continuous cases. Further, we investigate the exponential and logarithmic convexity of the differences between the left-hand side and the right-hand side of these inequalities and present several families of functions for which these results can be applied. Hindawi Publishing Corporation 2014-08-14 /pmc/articles/PMC4897212/ /pubmed/27379320 http://dx.doi.org/10.1155/2014/580605 Text en Copyright © 2014 Rabia Bibi et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Bibi, Rabia
Pečarić, Josip
Lipanović, Mirna Rodić
Improvements of Jensen-Type Inequalities for Diamond-α Integrals
title Improvements of Jensen-Type Inequalities for Diamond-α Integrals
title_full Improvements of Jensen-Type Inequalities for Diamond-α Integrals
title_fullStr Improvements of Jensen-Type Inequalities for Diamond-α Integrals
title_full_unstemmed Improvements of Jensen-Type Inequalities for Diamond-α Integrals
title_short Improvements of Jensen-Type Inequalities for Diamond-α Integrals
title_sort improvements of jensen-type inequalities for diamond-α integrals
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4897212/
https://www.ncbi.nlm.nih.gov/pubmed/27379320
http://dx.doi.org/10.1155/2014/580605
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