| A New Proof of the Stronger Second Mean Value Theorem for Integrals |
| Received:November 09, 2020 Revised:January 03, 2021 |
| Key Words:
second mean value theorem for integrals Riemann integrable Lebesgue integrable
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| Fund Project:Supported by Natural Science Basic Research Program of Shaanxi (Program No.2021JM-487), the Special Scientific Research Program of the Education Department of Shaanxi Province (Grant No.18JK0161) and the Scientific Research Foundation of Shaanxi University of Technology (Grant No.SLGQD1807). |
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| Abstract: |
| R. Witula et al obtained a stronger version of the second mean value theorem for integral with some restrictions. In this paper, the stronger version theorem is proved without any restriction. The result is first restricted to the Riemann integrable functions and can be easily generalized to $L^p$ integrable functions by using the well-known result that continuous functions are dense in the Banach space $L^p[a,b]$ for any $p \geq 1$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2021.03.004 |
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