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Certain Simpson's and Newton's type inequalities in Quantum Multiplicative Calculus | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 04 آبان 1405 اصل مقاله (1.47 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.70977.3556 | ||
| نویسندگان | ||
| Shilpi Jain1؛ Mubashir Hussain2؛ Abdul Mateen3؛ Praveen Agarwal* 4؛ Haibo Chen2 | ||
| 1Department of Mathematics, Poornima College of Engineering, Jaipur 302022, India. | ||
| 2School of Mathematics and Statistics, Central South University, Changsha 410083, China. | ||
| 3School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China. | ||
| 41. Department of Mathematical Science, Saveetha School of Engineering, Chennai, Tamilnadu, 602105 India. 2. Faculty of Science, Department of Computer Sciences, Karadeniz Technical University, Trabzon, Türkiye. 3. Scientific Research Centre, Baku Engineering University, Baku AZ0102, Azerbaijan. 4. International Telematic University Uninettuno, Corso Vittorio Emanuele II, 00186 Rome, Italy. | ||
| چکیده | ||
| This paper investigates the application of quantum multiplicative calculus to establish novel variants of Simpson's and Newton's type inequalities for quantum multiplicative differentiable functions. The motivation for employing multiplicative calculus lies in its ability to model discrete structure, proportional changes and exponential growth more effectively than classical calculus, making it a powerful framework for analyzing phenomena governed by discrete and multiplicative dynamics. The study derives two fundamental integral identities, which form the foundation for these new inequalities. Utilizing concepts from multiplicative convexity theory and Hölder's inequality, sharper and more generalized bounds are obtained. The proposed inequalities provide refined error estimates for quadrature rules, enhancing the precision of numerical integration methods. Numerical and graphical analyses are presented to validate the theoretical findings and demonstrate their practical utility. These results contribute to a deeper understanding of inequalities in multiplicative and quantum calculus, with implications for future research in integral inequalities, optimization, and numerical analysis. | ||
| کلیدواژه‌ها | ||
| Q-Calculus؛ Multiplicative Calculus؛ Simpson’s inequality | ||
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آمار تعداد مشاهده مقاله: 10 تعداد دریافت فایل اصل مقاله: 11 |
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