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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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Maragheh
2025-01-01
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| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | https://scma.maragheh.ac.ir/article_719367_b1e19bb13f87083fe83999b62323ee13.pdf |
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| Summary: | 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. |
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| ISSN: | 2322-5807 2423-3900 |