| 一个新的积分不等式及其应用 |
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| 引用本文： | 乔希民,罗俊丽.一个新的积分不等式及其应用[J].西安文理学院学报,2005,8(4):16-18. |
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| 作者姓名： | 乔希民 罗俊丽 |
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| 作者单位： | 商洛师范专科学校数学系,陕西商洛726000 |
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| 基金项目： | 全国教育科学“十五”规划重点课题（EHA030431） |
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| 摘 要： | 从离散型W．H．Young不等式出发，以归纳类比和分类讨论思想为基础，得到了一个新的积分不等式，并运用构造性方法给出了一种十分简洁的证明，又进一步讨论了新的积分不等式与P．Schweitzer反向积分不等式的关系，同时指出了由新的积分不等式能够得到Hoelder积分不等式、Minkowski积分不等式及Buniakowski—Schwarz积分不等式等，凸显其内在规律性和应用的广泛性。
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| 关 键 词： | W．H．Young不等式 新的积分不等式 构造性方法 |
| 文章编号： | 1008-5564(2005)02-0016-03 |
| 收稿时间： | 06 20 2005 12:00AM |
| 修稿时间： | 2005年6月20日 |
A New Integral Inequality and Its Application |
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| QIAO Xi-min, LUO Jun-li.A New Integral Inequality and Its Application[J].Journal of Xi‘an University of Arts & Science:Natural Science Edition,2005,8(4):16-18. |
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| Authors: | QIAO Xi-min LUO Jun-li |
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| Institution: | Department of Mathematics, Shangluo Teachers College, Shangluo 726000, China |
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| Abstract: | From the famous discrete W.H.Young's inequality,by induction and analogy as well as the principle of group discussion,a new integral inequality is obtained.With constructive method,a very simple proof is given.Then the relation between the new integral inequality and the famous P.Schweitzer reversal integral inequality is discussed.Meanwhile,it is pointed out that H?lder integral inequality,Minkowski integral inequality and Buniakowski-Schwarzon integral inequality can all be obtained from the new integral inequality,indicating its extensiveness in inner rules and application. |
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| Keywords: | W H Young's inequality a new integral inequality application constructive method |
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