Some New Hermite–Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral

In this investigation, for convex functions, some new [Formula: see text] –Hermite–Hadamard-type inequalities using the notions of [Formula: see text] derivative and [Formula: see text] integral are obtained. Furthermore, for [Formula: see text]-differentiable convex functions, some new ([Formula: s...

Descripción completa

Detalles Bibliográficos
Autores principales: Vivas-Cortez, Miguel, Ali, Muhammad Aamir, Budak, Hüseyin, Kalsoom, Humaira, Agarwal, Praveen
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8305804/
https://www.ncbi.nlm.nih.gov/pubmed/34209714
http://dx.doi.org/10.3390/e23070828
_version_ 1783727659592712192
author Vivas-Cortez, Miguel
Ali, Muhammad Aamir
Budak, Hüseyin
Kalsoom, Humaira
Agarwal, Praveen
author_facet Vivas-Cortez, Miguel
Ali, Muhammad Aamir
Budak, Hüseyin
Kalsoom, Humaira
Agarwal, Praveen
author_sort Vivas-Cortez, Miguel
collection PubMed
description In this investigation, for convex functions, some new [Formula: see text] –Hermite–Hadamard-type inequalities using the notions of [Formula: see text] derivative and [Formula: see text] integral are obtained. Furthermore, for [Formula: see text]-differentiable convex functions, some new ([Formula: see text]) estimates for midpoint and trapezoidal-type inequalities using the notions of [Formula: see text] integral are offered. It is also shown that the newly proved results for [Formula: see text] and [Formula: see text] can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.
format Online
Article
Text
id pubmed-8305804
institution National Center for Biotechnology Information
language English
publishDate 2021
publisher MDPI
record_format MEDLINE/PubMed
spelling pubmed-83058042021-07-25 Some New Hermite–Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral Vivas-Cortez, Miguel Ali, Muhammad Aamir Budak, Hüseyin Kalsoom, Humaira Agarwal, Praveen Entropy (Basel) Article In this investigation, for convex functions, some new [Formula: see text] –Hermite–Hadamard-type inequalities using the notions of [Formula: see text] derivative and [Formula: see text] integral are obtained. Furthermore, for [Formula: see text]-differentiable convex functions, some new ([Formula: see text]) estimates for midpoint and trapezoidal-type inequalities using the notions of [Formula: see text] integral are offered. It is also shown that the newly proved results for [Formula: see text] and [Formula: see text] can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities. MDPI 2021-06-29 /pmc/articles/PMC8305804/ /pubmed/34209714 http://dx.doi.org/10.3390/e23070828 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Vivas-Cortez, Miguel
Ali, Muhammad Aamir
Budak, Hüseyin
Kalsoom, Humaira
Agarwal, Praveen
Some New Hermite–Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral
title Some New Hermite–Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral
title_full Some New Hermite–Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral
title_fullStr Some New Hermite–Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral
title_full_unstemmed Some New Hermite–Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral
title_short Some New Hermite–Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral
title_sort some new hermite–hadamard and related inequalities for convex functions via (p,q)-integral
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8305804/
https://www.ncbi.nlm.nih.gov/pubmed/34209714
http://dx.doi.org/10.3390/e23070828
work_keys_str_mv AT vivascortezmiguel somenewhermitehadamardandrelatedinequalitiesforconvexfunctionsviapqintegral
AT alimuhammadaamir somenewhermitehadamardandrelatedinequalitiesforconvexfunctionsviapqintegral
AT budakhuseyin somenewhermitehadamardandrelatedinequalitiesforconvexfunctionsviapqintegral
AT kalsoomhumaira somenewhermitehadamardandrelatedinequalitiesforconvexfunctionsviapqintegral
AT agarwalpraveen somenewhermitehadamardandrelatedinequalitiesforconvexfunctionsviapqintegral

Ejemplares similares