关于詹森 - 沙玛 - 米塔尔型和杰弗里斯 - 沙玛 - 米塔尔型散度的不等式。
Inequalities for Jensen-Sharma-Mittal and Jeffreys-Sharma-Mittal Type -Divergences.
作者信息
Kluza Paweł A
机构信息
Department of Applied Mathematics and Computer Science, University of Life Sciences in Lublin, 28 Głęboka Street, 20-612 Lublin, Poland.
出版信息
Entropy (Basel). 2021 Dec 16;23(12):1688. doi: 10.3390/e23121688.
In this paper, we introduce new divergences called Jensen-Sharma-Mittal and Jeffreys-Sharma-Mittal in relation to convex functions. Some theorems, which give the lower and upper bounds for two new introduced divergences, are provided. The obtained results imply some new inequalities corresponding to known divergences. Some examples, which show that these are the generalizations of Rényi, Tsallis, and Kullback-Leibler types of divergences, are provided in order to show a few applications of new divergences.
在本文中，我们引入了与凸函数相关的新散度，即詹森 - 沙玛 - 米塔尔散度和杰弗里斯 - 沙玛 - 米塔尔散度。给出了一些定理，这些定理给出了两个新引入散度的上下界。所得结果蕴含了一些与已知散度相对应的新不等式。为了展示新散度的一些应用，给出了一些例子，这些例子表明它们是雷尼、Tsallis 和库尔贝克 - 莱布勒类型散度的推广。
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