Some Parameterized Quantum Midpoint and Quantum Trapezoid Type Inequalities for Convex Functions with Applications

Some Parameterized Quantum Midpoint and Quantum Trapezoid Type Inequalities for Convex Functions with Applications

Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and entropy, has various applications for quantum calculus. Inequalities and entropy functions have a strong association with convex functions. In this study, we prove...

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Bibliographic Details
Main Authors: Suphawat Asawasamrit, Muhammad Aamir Ali, Sotiris K. Ntouyas, Jessada Tariboon
Format: Article
Language:English
Published: MDPI AG 2021-07-01
Series:Entropy
Subjects:
Hermite–Hadamard inequality
midpoint and trapezoid inequalities
<i>q</i>-calculus
convex functions
Online Access:https://www.mdpi.com/1099-4300/23/8/996
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spelling doaj-a40710fce00f404e8a22231f39384daf2021-08-26T13:44:08ZengMDPI AGEntropy1099-43002021-07-012399699610.3390/e23080996Some Parameterized Quantum Midpoint and Quantum Trapezoid Type Inequalities for Convex Functions with ApplicationsSuphawat Asawasamrit0Muhammad Aamir Ali1Sotiris K. Ntouyas2Jessada Tariboon3Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandJiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, ChinaDepartment of Mathematics, University of Ioannina, 451 10 Ioannina, GreeceIntelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandQuantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and entropy, has various applications for quantum calculus. Inequalities and entropy functions have a strong association with convex functions. In this study, we prove quantum midpoint type inequalities, quantum trapezoidal type inequalities, and the quantum Simpson’s type inequality for differentiable convex functions using a new parameterized <i>q</i>-integral equality. The newly formed inequalities are also proven to be generalizations of previously existing inequities. Finally, using the newly established inequalities, we present some applications for quadrature formulas.https://www.mdpi.com/1099-4300/23/8/996Hermite–Hadamard inequalitymidpoint and trapezoid inequalities<i>q</i>-calculusconvex functions
collection DOAJ
language English
format Article
sources DOAJ
author Suphawat Asawasamrit
Muhammad Aamir Ali
Sotiris K. Ntouyas
Jessada Tariboon
spellingShingle Suphawat Asawasamrit
Muhammad Aamir Ali
Sotiris K. Ntouyas
Jessada Tariboon
Some Parameterized Quantum Midpoint and Quantum Trapezoid Type Inequalities for Convex Functions with Applications
Entropy
Hermite–Hadamard inequality
midpoint and trapezoid inequalities
<i>q</i>-calculus
convex functions
author_facet Suphawat Asawasamrit
Muhammad Aamir Ali
Sotiris K. Ntouyas
Jessada Tariboon
author_sort Suphawat Asawasamrit
title Some Parameterized Quantum Midpoint and Quantum Trapezoid Type Inequalities for Convex Functions with Applications
title_short Some Parameterized Quantum Midpoint and Quantum Trapezoid Type Inequalities for Convex Functions with Applications
title_full Some Parameterized Quantum Midpoint and Quantum Trapezoid Type Inequalities for Convex Functions with Applications
title_fullStr Some Parameterized Quantum Midpoint and Quantum Trapezoid Type Inequalities for Convex Functions with Applications
title_full_unstemmed Some Parameterized Quantum Midpoint and Quantum Trapezoid Type Inequalities for Convex Functions with Applications
title_sort some parameterized quantum midpoint and quantum trapezoid type inequalities for convex functions with applications
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2021-07-01
description Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and entropy, has various applications for quantum calculus. Inequalities and entropy functions have a strong association with convex functions. In this study, we prove quantum midpoint type inequalities, quantum trapezoidal type inequalities, and the quantum Simpson’s type inequality for differentiable convex functions using a new parameterized <i>q</i>-integral equality. The newly formed inequalities are also proven to be generalizations of previously existing inequities. Finally, using the newly established inequalities, we present some applications for quadrature formulas.
topic Hermite–Hadamard inequality
midpoint and trapezoid inequalities
<i>q</i>-calculus
convex functions
url https://www.mdpi.com/1099-4300/23/8/996
work_keys_str_mv AT suphawatasawasamrit someparameterizedquantummidpointandquantumtrapezoidtypeinequalitiesforconvexfunctionswithapplications
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AT sotiriskntouyas someparameterizedquantummidpointandquantumtrapezoidtypeinequalitiesforconvexfunctionswithapplications
AT jessadatariboon someparameterizedquantummidpointandquantumtrapezoidtypeinequalitiesforconvexfunctionswithapplications
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