New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex Functions
The main objective of this paper is to establish some new inequalities related to the open Newton-Cotes formulas in the setting of q-calculus. We establish a quantum integral identity first and then prove the desired inequalities for $q$-differentiable convex functions. These inequalities are useful...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2025-01-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_719367_b1e19bb13f87083fe83999b62323ee13.pdf |
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| author | Jarunee Soontharanon Muhammad Ali Shahram Rezapour Muhammad Toseef Thanin Sitthiwirattham |
| author_facet | Jarunee Soontharanon Muhammad Ali Shahram Rezapour Muhammad Toseef Thanin Sitthiwirattham |
| author_sort | Jarunee Soontharanon |
| collection | DOAJ |
| description | The main objective of this paper is to establish some new inequalities related to the open Newton-Cotes formulas in the setting of q-calculus. We establish a quantum integral identity first and then prove the desired inequalities for $q$-differentiable convex functions. These inequalities are useful for determining error bounds for the open Newton-Cotes formulas in both classical and $q$-calculus. This work distinguishes itself from existing studies by employing quantum operators, leading to sharper and more precise error estimates. These results extend the applicability of Newton-Cotes methods to quantum calculus, offering a novel contribution to the numerical analysis of convex functions. Finally, we provide mathematical examples and computational analysis to validate the newly established inequalities. |
| format | Article |
| id | doaj-art-2e26eda45027428e8b35afeafc0eb1fb |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-2e26eda45027428e8b35afeafc0eb1fb2025-02-11T05:28:01ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002025-01-0122120521910.22130/scma.2024.2036770.1826719367New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex FunctionsJarunee Soontharanon0Muhammad Ali1Shahram Rezapour2Muhammad Toseef3Thanin Sitthiwirattham4Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand.Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China.Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China.Research Group for Fractional Calculus Theory and Applications, Science and Technology Research Institute, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand.The main objective of this paper is to establish some new inequalities related to the open Newton-Cotes formulas in the setting of q-calculus. We establish a quantum integral identity first and then prove the desired inequalities for $q$-differentiable convex functions. These inequalities are useful for determining error bounds for the open Newton-Cotes formulas in both classical and $q$-calculus. This work distinguishes itself from existing studies by employing quantum operators, leading to sharper and more precise error estimates. These results extend the applicability of Newton-Cotes methods to quantum calculus, offering a novel contribution to the numerical analysis of convex functions. Finally, we provide mathematical examples and computational analysis to validate the newly established inequalities.https://scma.maragheh.ac.ir/article_719367_b1e19bb13f87083fe83999b62323ee13.pdfopen newton-cotes formulasconvex functionsq-calculusfractional inequalities |
| spellingShingle | Jarunee Soontharanon Muhammad Ali Shahram Rezapour Muhammad Toseef Thanin Sitthiwirattham New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex Functions Sahand Communications in Mathematical Analysis open newton-cotes formulas convex functions q-calculus fractional inequalities |
| title | New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex Functions |
| title_full | New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex Functions |
| title_fullStr | New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex Functions |
| title_full_unstemmed | New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex Functions |
| title_short | New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex Functions |
| title_sort | new forms of the open newton cotes type inequalities for a family of the quantum differentiable convex functions |
| topic | open newton-cotes formulas convex functions q-calculus fractional inequalities |
| url | https://scma.maragheh.ac.ir/article_719367_b1e19bb13f87083fe83999b62323ee13.pdf |
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