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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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/8/996 |
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| author | Suphawat Asawasamrit Muhammad Aamir Ali Sotiris K. Ntouyas Jessada Tariboon |
| author_facet | Suphawat Asawasamrit Muhammad Aamir Ali Sotiris K. Ntouyas Jessada Tariboon |
| author_sort | Suphawat Asawasamrit |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T08:49:58Z |
| format | Article |
| id | doaj.art-a40710fce00f404e8a22231f39384daf |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T08:49:58Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-a40710fce00f404e8a22231f39384daf2023-11-22T07:34:48ZengMDPI AGEntropy1099-43002021-07-0123899610.3390/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 |
| 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 |
| title | 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_short | 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 |
| topic | Hermite–Hadamard inequality midpoint and trapezoid inequalities <i>q</i>-calculus convex functions |
| url | https://www.mdpi.com/1099-4300/23/8/996 |
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