Triple Diamond-Alpha integral and Hölder-type inequalities

In this paper, we first introduce the definition of triple Diamond-Alpha integral for functions of three variables. Therefore, we present the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral on time scales, and then we obtain some new generalizations of the Hölder and rev...

Descripción completa

Detalles Bibliográficos
Autor principal: Tian, Jing-Feng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5945758/
https://www.ncbi.nlm.nih.gov/pubmed/29773929
http://dx.doi.org/10.1186/s13660-018-1704-0
_version_ 1783322052273373184
author Tian, Jing-Feng
author_facet Tian, Jing-Feng
author_sort Tian, Jing-Feng
collection PubMed
description In this paper, we first introduce the definition of triple Diamond-Alpha integral for functions of three variables. Therefore, we present the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral on time scales, and then we obtain some new generalizations of the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral. Moreover, using the obtained results, we give a new generalization of the Minkowski inequality for the triple Diamond-Alpha integral on time scales.
format Online
Article
Text
id pubmed-5945758
institution National Center for Biotechnology Information
language English
publishDate 2018
publisher Springer International Publishing
record_format MEDLINE/PubMed
spelling pubmed-59457582018-05-15 Triple Diamond-Alpha integral and Hölder-type inequalities Tian, Jing-Feng J Inequal Appl Research In this paper, we first introduce the definition of triple Diamond-Alpha integral for functions of three variables. Therefore, we present the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral on time scales, and then we obtain some new generalizations of the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral. Moreover, using the obtained results, we give a new generalization of the Minkowski inequality for the triple Diamond-Alpha integral on time scales. Springer International Publishing 2018-05-10 2018 /pmc/articles/PMC5945758/ /pubmed/29773929 http://dx.doi.org/10.1186/s13660-018-1704-0 Text en © The Author(s) 2018 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
Tian, Jing-Feng
Triple Diamond-Alpha integral and Hölder-type inequalities
title Triple Diamond-Alpha integral and Hölder-type inequalities
title_full Triple Diamond-Alpha integral and Hölder-type inequalities
title_fullStr Triple Diamond-Alpha integral and Hölder-type inequalities
title_full_unstemmed Triple Diamond-Alpha integral and Hölder-type inequalities
title_short Triple Diamond-Alpha integral and Hölder-type inequalities
title_sort triple diamond-alpha integral and hölder-type inequalities
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5945758/
https://www.ncbi.nlm.nih.gov/pubmed/29773929
http://dx.doi.org/10.1186/s13660-018-1704-0
work_keys_str_mv AT tianjingfeng triplediamondalphaintegralandholdertypeinequalities

Ejemplares similares