| Aczel不等式的推广 |
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| 引用本文： | 楼宇同. Aczel不等式的推广[J]. 南京航空航天大学学报, 1991, 0(2) |
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| 作者姓名： | 楼宇同 |
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| 作者单位： | 南京航空学院数理力学系 |
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| 摘 要： | 在Mitrinovie,D.S.著的《解析不等式》中介绍了有名的Aczel不等式、Popoviciu不等式、Bellman不等式,但后者的不等式的条件不妥当,且也没有给出等式成立的充要条件。本文进一步推广Aczel不等式,并改进了Popoviciu不等式与Bellman不等式的条件,也给出了等式成立的充要条件,且把Aczel不等式推广到复向量空间中,也推广到相反的不等式。
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| 关 键 词： | 数学分析 不等式 凸函数 复数辐角 充要条件 数学归纳法 推论 |
Generalization of Aczel Inequalities |
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| Lou Yutong. Generalization of Aczel Inequalities[J]. Journal of Nanjing University of Aeronautics & Astronautics, 1991, 0(2) |
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| Authors: | Lou Yutong |
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| Abstract: | D. S. Mitrinovic has introduced the well-known Aczel's inequalities in his book titled Analytic inequalities, the T. Popoviciu's inequality and the R.Bellman's inequality. The conditions of the latter inequalities are not appropriate and the necessary and sufficient conditions of the equality are also not given.In this paper the Aczel inequalities are further generalized and the conditions of Popoviciu's and Bellman's inequalities are modified, the necessary and sufficient conditions of the equality are also given. The Aczel's inequalities are generalized into the complex linear vector space as well as to the contrary inequalities. |
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| Keywords: | mathematical analysis inequalities convex functions argument of a complex number necessary and sufficient conditions mathematical induction corollary |
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