Properties and Applications of Symmetric Quantum Calculus
Symmetric derivatives and integrals are extensively studied to overcome the limitations of classical derivatives and integral operators. In the current investigation, we explore the quantum symmetric derivatives on finite intervals. We introduced the idea of right quantum symmetric derivatives and i...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/2/107 |
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| author | Miguel Vivas-Cortez Muhammad Zakria Javed Muhammad Uzair Awan Silvestru Sever Dragomir Ahmed M. Zidan |
| author_facet | Miguel Vivas-Cortez Muhammad Zakria Javed Muhammad Uzair Awan Silvestru Sever Dragomir Ahmed M. Zidan |
| author_sort | Miguel Vivas-Cortez |
| collection | DOAJ |
| description | Symmetric derivatives and integrals are extensively studied to overcome the limitations of classical derivatives and integral operators. In the current investigation, we explore the quantum symmetric derivatives on finite intervals. We introduced the idea of right quantum symmetric derivatives and integral operators and studied various properties of both operators as well. Using these concepts, we deliver new variants of Young’s inequality, Hölder’s inequality, Minkowski’s inequality, Hermite–Hadamard’s inequality, Ostrowski’s inequality, and Gruss–Chebysev inequality. We report the Hermite–Hadamard’s inequalities by taking into account the differentiability of convex mappings. These fundamental results are pivotal to studying the various other problems in the field of inequalities. The validation of results is also supported with some visuals. |
| first_indexed | 2024-03-07T22:31:39Z |
| format | Article |
| id | doaj.art-6850406016684d148d8ffaf2f81d9a8d |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-07T22:31:39Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-6850406016684d148d8ffaf2f81d9a8d2024-02-23T15:17:14ZengMDPI AGFractal and Fractional2504-31102024-02-018210710.3390/fractalfract8020107Properties and Applications of Symmetric Quantum CalculusMiguel Vivas-Cortez0Muhammad Zakria Javed1Muhammad Uzair Awan2Silvestru Sever Dragomir3Ahmed M. Zidan4Escuela 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, Government College University, Faisalabad 38000, PakistanDepartment of Mathematics, Government College University, Faisalabad 38000, PakistanMathematics, College of Engineering & Science, Victoria University, P.O. Box 14428, Melbourne City, VIC 8001, AustraliaDepartment of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi ArabiaSymmetric derivatives and integrals are extensively studied to overcome the limitations of classical derivatives and integral operators. In the current investigation, we explore the quantum symmetric derivatives on finite intervals. We introduced the idea of right quantum symmetric derivatives and integral operators and studied various properties of both operators as well. Using these concepts, we deliver new variants of Young’s inequality, Hölder’s inequality, Minkowski’s inequality, Hermite–Hadamard’s inequality, Ostrowski’s inequality, and Gruss–Chebysev inequality. We report the Hermite–Hadamard’s inequalities by taking into account the differentiability of convex mappings. These fundamental results are pivotal to studying the various other problems in the field of inequalities. The validation of results is also supported with some visuals.https://www.mdpi.com/2504-3110/8/2/107convexfunctionHermite–HadamardHolder’ssymmetricquantum |
| spellingShingle | Miguel Vivas-Cortez Muhammad Zakria Javed Muhammad Uzair Awan Silvestru Sever Dragomir Ahmed M. Zidan Properties and Applications of Symmetric Quantum Calculus Fractal and Fractional convex function Hermite–Hadamard Holder’s symmetric quantum |
| title | Properties and Applications of Symmetric Quantum Calculus |
| title_full | Properties and Applications of Symmetric Quantum Calculus |
| title_fullStr | Properties and Applications of Symmetric Quantum Calculus |
| title_full_unstemmed | Properties and Applications of Symmetric Quantum Calculus |
| title_short | Properties and Applications of Symmetric Quantum Calculus |
| title_sort | properties and applications of symmetric quantum calculus |
| topic | convex function Hermite–Hadamard Holder’s symmetric quantum |
| url | https://www.mdpi.com/2504-3110/8/2/107 |
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