$On $\mathscr{M}$-convex functions$

On $\mathscr{M}$-convex functions

In this article, we introduce the notion of $\mathscr{M}$-convex functions, $\log$-$\mathscr{M}$-convex functions and the notion of quasi $\mathscr{M}$-convex functions. We derive some new analogues of Hermite-Hadamard like inequalities associated with $\mathscr{M}$-convex functions by using the con...

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Main Authors:	Muhammad Uzair Awan, Muhammad Aslam Noor, Tingsong Du, Khalida Inayat Noor
Format:	Article
Language:	English
Published:	AIMS Press 2020-03-01
Series:	AIMS Mathematics
Subjects:	convex $\mathscr{m}$-convex $\log$-$\mathscr{m}$-convex quasi $\mathscr{m}$-convex hermite-hadamard inequality fractional quantum
Online Access:	https://www.aimspress.com/article/10.3934/math.2020157/fulltext.html

id	doaj-be78a5dfc6764c2b84ac778bf0e0762c
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spelling	doaj-be78a5dfc6764c2b84ac778bf0e0762c2020-11-25T04:04:45ZengAIMS PressAIMS Mathematics2473-69882020-03-01532376238710.3934/math.2020157On $\mathscr{M}$-convex functionsMuhammad Uzair Awan0Muhammad Aslam Noor1Tingsong Du2Khalida Inayat Noor31 Department of Mathematics, GC University, Faisalabad, Pakistan2 Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan3 Department of Mathematics, College of Science, China Three Gorges University, China2 Department of Mathematics, COMSATS University Islamabad, Islamabad, PakistanIn this article, we introduce the notion of $\mathscr{M}$-convex functions, $\log$-$\mathscr{M}$-convex functions and the notion of quasi $\mathscr{M}$-convex functions. We derive some new analogues of Hermite-Hadamard like inequalities associated with $\mathscr{M}$-convex functions by using the concepts of ordinary, fractional and quantum calculus. The main results of this paper may be useful where bounds for natural phenomena described by integrals such as mechanical work are frequently required. These results are also helpful in the field of numerical analysis where error analysis is required.https://www.aimspress.com/article/10.3934/math.2020157/fulltext.htmlconvex$\mathscr{m}$-convex$\log$-$\mathscr{m}$-convexquasi $\mathscr{m}$-convexhermite-hadamard inequalityfractionalquantum
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Muhammad Uzair Awan Muhammad Aslam Noor Tingsong Du Khalida Inayat Noor
spellingShingle	Muhammad Uzair Awan Muhammad Aslam Noor Tingsong Du Khalida Inayat Noor On $\mathscr{M}$-convex functions AIMS Mathematics convex $\mathscr{m}$-convex $\log$-$\mathscr{m}$-convex quasi $\mathscr{m}$-convex hermite-hadamard inequality fractional quantum
author_facet	Muhammad Uzair Awan Muhammad Aslam Noor Tingsong Du Khalida Inayat Noor
author_sort	Muhammad Uzair Awan
title	On $\mathscr{M}$-convex functions
title_short	On $\mathscr{M}$-convex functions
title_full	On $\mathscr{M}$-convex functions
title_fullStr	On $\mathscr{M}$-convex functions
title_full_unstemmed	On $\mathscr{M}$-convex functions
title_sort	on $\mathscr{m}$-convex functions
publisher	AIMS Press
series	AIMS Mathematics
issn	2473-6988
publishDate	2020-03-01
description	In this article, we introduce the notion of $\mathscr{M}$-convex functions, $\log$-$\mathscr{M}$-convex functions and the notion of quasi $\mathscr{M}$-convex functions. We derive some new analogues of Hermite-Hadamard like inequalities associated with $\mathscr{M}$-convex functions by using the concepts of ordinary, fractional and quantum calculus. The main results of this paper may be useful where bounds for natural phenomena described by integrals such as mechanical work are frequently required. These results are also helpful in the field of numerical analysis where error analysis is required.
topic	convex $\mathscr{m}$-convex $\log$-$\mathscr{m}$-convex quasi $\mathscr{m}$-convex hermite-hadamard inequality fractional quantum
url	https://www.aimspress.com/article/10.3934/math.2020157/fulltext.html
work_keys_str_mv	AT muhammaduzairawan onmathscrmconvexfunctions AT muhammadaslamnoor onmathscrmconvexfunctions AT tingsongdu onmathscrmconvexfunctions AT khalidainayatnoor onmathscrmconvexfunctions
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On $\mathscr{M}$-convex functions

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