تقرير
On the monotonicity of left and right Riemann sums
| العنوان: | On the monotonicity of left and right Riemann sums |
|---|---|
| المؤلفون: | Bouthat, Ludovick |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Classical Analysis and ODEs, 26D15, 26A48, 26A42, 41A05 |
| الوصف: | Riemann sums, a classical method for approximating the definite integral of a function, have been extensively studied in the past. However, their monotonic properties, while still of great importance, particularly in approximation theory and interpolation theory, remain somewhat obscure. This paper is dedicated to proving general theorems about the monotonicity of left and right Riemann sums, a problem first raised by Fej\'er in 1950. We provide a much-needed review of the literature on the problem and offer several new sufficient and necessary conditions for the monotonicity of Riemann sums. Additionally, we present a new insightful proof of a fundamental theorem related to these sums using tools from the theory of majorization. The author also delves deeper into a question posed by Borwein, almost resolving it completely. Comment: 35 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2311.01208 |
| رقم الأكسشن: | edsarx.2311.01208 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |