n方凸函数的性质与Jensen型不等式
首发时间:2015-04-17
摘要:本文在已有研究的基础之上,首先给出了n方凸函数的定义,然后利用n方凸函数的函数凸性,以及运用凸函数及平方凸函数的研究方法,给出了n方凸函数的判定定理及其性质,并进一步给出了Jensen型不等式,推广已有的一些结果。
关键词: n方凸函数 Jensen型不等式 单调性
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Properties of power n-convex function and Jensen-type inequality
Abstract:In this paper, on the basis of previous researches, firstly, the definition of power n-convex function are given. Secondly, using convex function of the power n-convex functions, and the use of research methods of convex function and square-convex function, gives the power n-convex function theorem and its properties, and further set up the Jensen-type inequality. Lastly, some results are generalized the existing.
Keywords: n-convex function Jensen-type inequality Monotonicity
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