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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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 |
work_keys_str_mv |
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