文献类型：期刊文献

英文题名：The Choquet integral of log-convex functions

作者：Wang, Hongxia[1,2]

第一作者：王洪霞;Wang, Hongxia

通讯作者：Wang, HX[1];Wang, HX[2]

机构：[1]Henan Univ Econ & Law, Coll Stat, Zhengzhou, Henan, Peoples R China;[2]Anal & Res Ctr Educ & Statist Data Henan Prov, Zhengzhou, Henan, Peoples R China

第一机构：河南财经政法大学统计与大数据学院

通讯机构：[1]corresponding author), Henan Univ Econ & Law, Coll Stat, Zhengzhou, Henan, Peoples R China;[2]corresponding author), Anal & Res Ctr Educ & Statist Data Henan Prov, Zhengzhou, Henan, Peoples R China.|[1048415]河南财经政法大学统计与大数据学院;[10484]河南财经政法大学;

年份：2018

卷号：2018

外文期刊名：JOURNAL OF INEQUALITIES AND APPLICATIONS

收录：;Scopus(收录号：2-s2.0-85051723948);WOS:【SCI-EXPANDED(收录号:WOS:000442296400003)】；

基金：This work is supported by the Scientific Research Foundation for Doctors of Henan University of Economics and Law, and by the University Key Research Project of Henan Province, China (18A110011).

语种：英文

外文关键词：Choquet integral; Log-convex function; Inequality

摘要：In this paper we investigate the upper bound and the lower bound of the Choquet integral for log-convex functions. Firstly, for a monotone log-convex function, we state the similar Hadamard inequality of the Choquet integral in the framework of distorted measure. Secondly, we estimate the upper bound of the Choquet integral for a general log-convex function, respectively, in the case of distorted Lebesgue measure and in the non-additive measure. Finally, we present Jensen's inequality of the Choquet integral for log-convex functions, which can be used to estimate the lower bound of this kind when the non-additive measure is concave. We provide some examples in the framework of the distorted Lebesgue measure to illustrate all the results.