Some New <i>q</i>—Integral Inequalities Using Generalized Quantum Montgomery Identity via Preinvex Functions

In this work the authors establish a new generalized version of Montgomery’s identity in the setting of quantum calculus. From this result, some new estimates of Ostrowski type inequalities are given using preinvex functions. Given the generality of preinvex functions, particular <inline-formula&...

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Main Authors: Miguel Vivas-Cortez, Artion Kashuri, Rozana Liko, Jorge E. Hernández Hernández
Format: Article
Language:English
Published: MDPI AG 2020-04-01
Series:Symmetry
Subjects:
Online Access:https://www.mdpi.com/2073-8994/12/4/553
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spelling doaj-485d3efe7abf48aa9c79fe73db756d8d2020-11-25T02:37:27ZengMDPI AGSymmetry2073-89942020-04-011255355310.3390/sym12040553Some New <i>q</i>—Integral Inequalities Using Generalized Quantum Montgomery Identity via Preinvex FunctionsMiguel Vivas-Cortez0Artion Kashuri1Rozana Liko2Jorge E. Hernández Hernández3Escuela de Ciencias Físicas y Matemáticas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Católica del Ecuador, Av. 12 de Octubre 1076. Apartado, Quito 17-01-2184, EcuadorDepartment of Mathematics, Faculty of Technical Science, University Ismail Qemali, L. Pavaresia, Vlora 1001, Vlore, AlbaniaDepartment of Mathematics, Faculty of Technical Science, University Ismail Qemali, L. Pavaresia, Vlora 1001, Vlore, AlbaniaDepartamento de Técnicas Cuantitativas, Decanato de Ciencias Económicas y Empresariales, Universidad Centroccidental Lisandro Alvarado, Av. 20. esq. Av. Moran, Edf. Los Militares, Piso 2, Ofc.2, Barquisimeto 3001, VenezuelaIn this work the authors establish a new generalized version of Montgomery’s identity in the setting of quantum calculus. From this result, some new estimates of Ostrowski type inequalities are given using preinvex functions. Given the generality of preinvex functions, particular <inline-formula> <math display="inline"> <semantics> <mrow> <mi>q</mi> </mrow> </semantics> </math> </inline-formula>—integral inequalities are established with appropriate choice of the parametric bifunction. Some new special cases from the main results are obtained and some known results are recaptured as well. At the end, a briefly conclusion is given.https://www.mdpi.com/2073-8994/12/4/553Quantum Montgomery identity<i>ϕ</i>-convex functionsintegral inequalities
collection DOAJ
language English
format Article
sources DOAJ
author Miguel Vivas-Cortez
Artion Kashuri
Rozana Liko
Jorge E. Hernández Hernández
spellingShingle Miguel Vivas-Cortez
Artion Kashuri
Rozana Liko
Jorge E. Hernández Hernández
Some New <i>q</i>—Integral Inequalities Using Generalized Quantum Montgomery Identity via Preinvex Functions
Symmetry
Quantum Montgomery identity
<i>ϕ</i>-convex functions
integral inequalities
author_facet Miguel Vivas-Cortez
Artion Kashuri
Rozana Liko
Jorge E. Hernández Hernández
author_sort Miguel Vivas-Cortez
title Some New <i>q</i>—Integral Inequalities Using Generalized Quantum Montgomery Identity via Preinvex Functions
title_short Some New <i>q</i>—Integral Inequalities Using Generalized Quantum Montgomery Identity via Preinvex Functions
title_full Some New <i>q</i>—Integral Inequalities Using Generalized Quantum Montgomery Identity via Preinvex Functions
title_fullStr Some New <i>q</i>—Integral Inequalities Using Generalized Quantum Montgomery Identity via Preinvex Functions
title_full_unstemmed Some New <i>q</i>—Integral Inequalities Using Generalized Quantum Montgomery Identity via Preinvex Functions
title_sort some new <i>q</i>—integral inequalities using generalized quantum montgomery identity via preinvex functions
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2020-04-01
description In this work the authors establish a new generalized version of Montgomery’s identity in the setting of quantum calculus. From this result, some new estimates of Ostrowski type inequalities are given using preinvex functions. Given the generality of preinvex functions, particular <inline-formula> <math display="inline"> <semantics> <mrow> <mi>q</mi> </mrow> </semantics> </math> </inline-formula>—integral inequalities are established with appropriate choice of the parametric bifunction. Some new special cases from the main results are obtained and some known results are recaptured as well. At the end, a briefly conclusion is given.
topic Quantum Montgomery identity
<i>ϕ</i>-convex functions
integral inequalities
url https://www.mdpi.com/2073-8994/12/4/553
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AT artionkashuri somenewiqiintegralinequalitiesusinggeneralizedquantummontgomeryidentityviapreinvexfunctions
AT rozanaliko somenewiqiintegralinequalitiesusinggeneralizedquantummontgomeryidentityviapreinvexfunctions
AT jorgeehernandezhernandez somenewiqiintegralinequalitiesusinggeneralizedquantummontgomeryidentityviapreinvexfunctions
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