Levinson’s type generalization of the Jensen inequality and its converse for real Stieltjes measure

We derive the Levinson type generalization of the Jensen and the converse Jensen inequality for real Stieltjes measure, not necessarily positive. As a consequence, also the Levinson type generalization of the Hermite-Hadamard inequality is obtained. Similarly, we derive the Levinson type generalizat...

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Detalles Bibliográficos
Autores principales: Mikić, Rozarija, Pečarić, Josip, Rodić, Mirna
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5209453/
https://www.ncbi.nlm.nih.gov/pubmed/28111504
http://dx.doi.org/10.1186/s13660-016-1274-y
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author Mikić, Rozarija
Pečarić, Josip
Rodić, Mirna
author_facet Mikić, Rozarija
Pečarić, Josip
Rodić, Mirna
author_sort Mikić, Rozarija
collection PubMed
description We derive the Levinson type generalization of the Jensen and the converse Jensen inequality for real Stieltjes measure, not necessarily positive. As a consequence, also the Levinson type generalization of the Hermite-Hadamard inequality is obtained. Similarly, we derive the Levinson type generalization of Giaccardi’s inequality. The obtained results are then applied for establishing new mean-value theorems. The results from this paper represent a generalization of several recent results.
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spelling pubmed-52094532017-01-18 Levinson’s type generalization of the Jensen inequality and its converse for real Stieltjes measure Mikić, Rozarija Pečarić, Josip Rodić, Mirna J Inequal Appl Research We derive the Levinson type generalization of the Jensen and the converse Jensen inequality for real Stieltjes measure, not necessarily positive. As a consequence, also the Levinson type generalization of the Hermite-Hadamard inequality is obtained. Similarly, we derive the Levinson type generalization of Giaccardi’s inequality. The obtained results are then applied for establishing new mean-value theorems. The results from this paper represent a generalization of several recent results. Springer International Publishing 2017-01-03 2017 /pmc/articles/PMC5209453/ /pubmed/28111504 http://dx.doi.org/10.1186/s13660-016-1274-y Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Mikić, Rozarija
Pečarić, Josip
Rodić, Mirna
Levinson’s type generalization of the Jensen inequality and its converse for real Stieltjes measure
title Levinson’s type generalization of the Jensen inequality and its converse for real Stieltjes measure
title_full Levinson’s type generalization of the Jensen inequality and its converse for real Stieltjes measure
title_fullStr Levinson’s type generalization of the Jensen inequality and its converse for real Stieltjes measure
title_full_unstemmed Levinson’s type generalization of the Jensen inequality and its converse for real Stieltjes measure
title_short Levinson’s type generalization of the Jensen inequality and its converse for real Stieltjes measure
title_sort levinson’s type generalization of the jensen inequality and its converse for real stieltjes measure
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5209453/
https://www.ncbi.nlm.nih.gov/pubmed/28111504
http://dx.doi.org/10.1186/s13660-016-1274-y
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