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。
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.
关键词
数学分析
不等式
凸函数
复数辐角
mathematical analysis, inequalities, convex functions, argument of a complex number, necessary and sufficient conditions, mathematical induction, corollary
