Integral inequalities for some convex functions via generalized fractional integrals

In this paper, we obtain the Hermite–Hadamard type inequalities for s-convex functions and m-convex functions via a generalized fractional integral, known as Katugampola fractional integral, which is the generalization of Riemann–Liouville fractional integral and Hadamard fractional integral. We sho...

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Detalles Bibliográficos
Autores principales: Mehreen, Naila, Anwar, Matloob
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6096909/
https://www.ncbi.nlm.nih.gov/pubmed/30839565
http://dx.doi.org/10.1186/s13660-018-1807-7
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author Mehreen, Naila
Anwar, Matloob
author_facet Mehreen, Naila
Anwar, Matloob
author_sort Mehreen, Naila
collection PubMed
description In this paper, we obtain the Hermite–Hadamard type inequalities for s-convex functions and m-convex functions via a generalized fractional integral, known as Katugampola fractional integral, which is the generalization of Riemann–Liouville fractional integral and Hadamard fractional integral. We show that through the Katugampola fractional integral we can find a Hermite–Hadamard inequality via the Riemann–Liouville fractional integral.
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spelling pubmed-60969092018-08-24 Integral inequalities for some convex functions via generalized fractional integrals Mehreen, Naila Anwar, Matloob J Inequal Appl Research In this paper, we obtain the Hermite–Hadamard type inequalities for s-convex functions and m-convex functions via a generalized fractional integral, known as Katugampola fractional integral, which is the generalization of Riemann–Liouville fractional integral and Hadamard fractional integral. We show that through the Katugampola fractional integral we can find a Hermite–Hadamard inequality via the Riemann–Liouville fractional integral. Springer International Publishing 2018-08-14 2018 /pmc/articles/PMC6096909/ /pubmed/30839565 http://dx.doi.org/10.1186/s13660-018-1807-7 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
Mehreen, Naila
Anwar, Matloob
Integral inequalities for some convex functions via generalized fractional integrals
title Integral inequalities for some convex functions via generalized fractional integrals
title_full Integral inequalities for some convex functions via generalized fractional integrals
title_fullStr Integral inequalities for some convex functions via generalized fractional integrals
title_full_unstemmed Integral inequalities for some convex functions via generalized fractional integrals
title_short Integral inequalities for some convex functions via generalized fractional integrals
title_sort integral inequalities for some convex functions via generalized fractional integrals
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6096909/
https://www.ncbi.nlm.nih.gov/pubmed/30839565
http://dx.doi.org/10.1186/s13660-018-1807-7
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AT anwarmatloob integralinequalitiesforsomeconvexfunctionsviageneralizedfractionalintegrals

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