The Choquet integral of log-convex functions

• Main Author: Hongxia Wang
• Format: Article
• Language: English
• Published: SpringerOpen 2018-08-01
• Series: Journal of Inequalities and Applications
• Subjects: Choquet integral; Log-convex function; Inequality
• Online Access: http://link.springer.com/article/10.1186/s13660-018-1803-y

Abstract 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.