New generalizations of Popoviciu-type inequalities via new Green’s functions and Montgomery identity

The inequality of Popoviciu, which was improved by Vasić and Stanković (Math. Balk. 6:281-288, 1976), is generalized by using new identities involving new Green’s functions. New generalizations of an improved Popoviciu inequality are obtained by using generalized Montgomery identity along with new G...

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Autores principales: Mehmood, Nasir, Agarwal, Ravi P, Butt, Saad Ihsan, Pečarić, Josip
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5423991/
https://www.ncbi.nlm.nih.gov/pubmed/28553058
http://dx.doi.org/10.1186/s13660-017-1379-y
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author Mehmood, Nasir
Agarwal, Ravi P
Butt, Saad Ihsan
Pečarić, Josip
author_facet Mehmood, Nasir
Agarwal, Ravi P
Butt, Saad Ihsan
Pečarić, Josip
author_sort Mehmood, Nasir
collection PubMed
description The inequality of Popoviciu, which was improved by Vasić and Stanković (Math. Balk. 6:281-288, 1976), is generalized by using new identities involving new Green’s functions. New generalizations of an improved Popoviciu inequality are obtained by using generalized Montgomery identity along with new Green’s functions. As an application, we formulate the monotonicity of linear functionals constructed from the generalized identities, utilizing the recent theory of inequalities for n-convex functions at a point. New upper bounds of Grüss and Ostrowski type are also computed.
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spelling pubmed-54239912017-05-25 New generalizations of Popoviciu-type inequalities via new Green’s functions and Montgomery identity Mehmood, Nasir Agarwal, Ravi P Butt, Saad Ihsan Pečarić, Josip J Inequal Appl Research The inequality of Popoviciu, which was improved by Vasić and Stanković (Math. Balk. 6:281-288, 1976), is generalized by using new identities involving new Green’s functions. New generalizations of an improved Popoviciu inequality are obtained by using generalized Montgomery identity along with new Green’s functions. As an application, we formulate the monotonicity of linear functionals constructed from the generalized identities, utilizing the recent theory of inequalities for n-convex functions at a point. New upper bounds of Grüss and Ostrowski type are also computed. Springer International Publishing 2017-05-10 2017 /pmc/articles/PMC5423991/ /pubmed/28553058 http://dx.doi.org/10.1186/s13660-017-1379-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
Mehmood, Nasir
Agarwal, Ravi P
Butt, Saad Ihsan
Pečarić, Josip
New generalizations of Popoviciu-type inequalities via new Green’s functions and Montgomery identity
title New generalizations of Popoviciu-type inequalities via new Green’s functions and Montgomery identity
title_full New generalizations of Popoviciu-type inequalities via new Green’s functions and Montgomery identity
title_fullStr New generalizations of Popoviciu-type inequalities via new Green’s functions and Montgomery identity
title_full_unstemmed New generalizations of Popoviciu-type inequalities via new Green’s functions and Montgomery identity
title_short New generalizations of Popoviciu-type inequalities via new Green’s functions and Montgomery identity
title_sort new generalizations of popoviciu-type inequalities via new green’s functions and montgomery identity
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5423991/
https://www.ncbi.nlm.nih.gov/pubmed/28553058
http://dx.doi.org/10.1186/s13660-017-1379-y
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