The Jensen inequality has many applications in several fields such as mathematics, statistics and economics etc. There are a lot of results devoted to the Jensen inequality concerning refinements, generalizations and converses etc. The main aim of this paper is to use new idea and present converses of the Jensen inequality with the help of Green functions. By virtue of these results, we obtain converses of Holder and Levinson’s inequalities. At the end we present several applications of these results in information theory. The idea used in this paper may stimulate further research for the Jensen inequality.

中文翻译：

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Jensen 不等式通过格林函数与应用程序的新反面

Jensen 不等式在数学、统计学和经济学等多个领域有很多应用。关于 Jensen 不等式的改进、推广和逆向等方面有很多成果。本文的主要目的是使用新的思想和呈现在格林函数的帮助下，詹森不等式的逆。凭借这些结果，我们获得了 Holder 和 Levinson 不等式的逆。最后，我们介绍了这些结果在信息论中的几种应用。本文中使用的想法可能会激发对 Jensen 不等式的进一步研究。