Exploration of Quantum Milne–Mercer-Type Inequalities with Applications
Quantum calculus provides a significant generalization of classical concepts and overcomes the limitations of classical calculus in tackling non-differentiable functions. Implementing the <i>q</i>-concepts to obtain fresh variants of classical outcomes is a very intriguing aspect of rese...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/5/1096 |
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| author | Bandar Bin-Mohsin Muhammad Zakria Javed Muhammad Uzair Awan Awais Gul Khan Clemente Cesarano Muhammad Aslam Noor |
| author_facet | Bandar Bin-Mohsin Muhammad Zakria Javed Muhammad Uzair Awan Awais Gul Khan Clemente Cesarano Muhammad Aslam Noor |
| author_sort | Bandar Bin-Mohsin |
| collection | DOAJ |
| description | Quantum calculus provides a significant generalization of classical concepts and overcomes the limitations of classical calculus in tackling non-differentiable functions. Implementing the <i>q</i>-concepts to obtain fresh variants of classical outcomes is a very intriguing aspect of research in mathematical analysis. The objective of this article is to establish novel Milne-type integral inequalities through the utilization of the Mercer inequality for <i>q</i>-differentiable convex mappings. In order to accomplish this task, we begin by demonstrating a new quantum identity of the Milne type linked to left and right <i>q</i> derivatives. This serves as a supporting result for our primary findings. Our approach involves using the <i>q</i>-equality, well-known inequalities, and convex mappings to obtain new error bounds of the Milne–Mercer type. We also provide some special cases, numerical examples, and graphical analysis to evaluate the efficacy of our results. To the best of our knowledge, this is the first article to focus on quantum Milne–Mercer-type inequalities and we hope that our methods and findings inspire readers to conduct further investigation into this problem. |
| first_indexed | 2024-03-11T03:16:22Z |
| format | Article |
| id | doaj.art-6ce3eca53b1a4c82afeb1b7200014367 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T03:16:22Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-6ce3eca53b1a4c82afeb1b72000143672023-11-18T03:30:53ZengMDPI AGSymmetry2073-89942023-05-01155109610.3390/sym15051096Exploration of Quantum Milne–Mercer-Type Inequalities with ApplicationsBandar Bin-Mohsin0Muhammad Zakria Javed1Muhammad Uzair Awan2Awais Gul Khan3Clemente Cesarano4Muhammad Aslam Noor5Department of Mathematics, College of Science, King Saud University, Riyadh 145111, Saudi ArabiaDepartment of Mathematics, Government College University, Faisalabad 54000, PakistanDepartment of Mathematics, Government College University, Faisalabad 54000, PakistanDepartment of Mathematics, Government College University, Faisalabad 54000, PakistanSection of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, ItalyDepartment of Mathematics, COMSATS University Islamabad, Islamabad 45550, PakistanQuantum calculus provides a significant generalization of classical concepts and overcomes the limitations of classical calculus in tackling non-differentiable functions. Implementing the <i>q</i>-concepts to obtain fresh variants of classical outcomes is a very intriguing aspect of research in mathematical analysis. The objective of this article is to establish novel Milne-type integral inequalities through the utilization of the Mercer inequality for <i>q</i>-differentiable convex mappings. In order to accomplish this task, we begin by demonstrating a new quantum identity of the Milne type linked to left and right <i>q</i> derivatives. This serves as a supporting result for our primary findings. Our approach involves using the <i>q</i>-equality, well-known inequalities, and convex mappings to obtain new error bounds of the Milne–Mercer type. We also provide some special cases, numerical examples, and graphical analysis to evaluate the efficacy of our results. To the best of our knowledge, this is the first article to focus on quantum Milne–Mercer-type inequalities and we hope that our methods and findings inspire readers to conduct further investigation into this problem.https://www.mdpi.com/2073-8994/15/5/1096convexquantumHermite–HadamardMilne–Mercerdifferentiable |
| spellingShingle | Bandar Bin-Mohsin Muhammad Zakria Javed Muhammad Uzair Awan Awais Gul Khan Clemente Cesarano Muhammad Aslam Noor Exploration of Quantum Milne–Mercer-Type Inequalities with Applications Symmetry convex quantum Hermite–Hadamard Milne–Mercer differentiable |
| title | Exploration of Quantum Milne–Mercer-Type Inequalities with Applications |
| title_full | Exploration of Quantum Milne–Mercer-Type Inequalities with Applications |
| title_fullStr | Exploration of Quantum Milne–Mercer-Type Inequalities with Applications |
| title_full_unstemmed | Exploration of Quantum Milne–Mercer-Type Inequalities with Applications |
| title_short | Exploration of Quantum Milne–Mercer-Type Inequalities with Applications |
| title_sort | exploration of quantum milne mercer type inequalities with applications |
| topic | convex quantum Hermite–Hadamard Milne–Mercer differentiable |
| url | https://www.mdpi.com/2073-8994/15/5/1096 |
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