Abstract
In this paper, we investigate the refinements of Jensen's inequalities in Choquet calculus and applications. We propose respectively one refinement of Theorem 3.3 – Jensen type inequality I and four refinements of Theorem 3.4 – Jensen type inequality II in Wang's article (Wang, 2011 [10]), and then use these refinements to prove other inequalities. It is specially mentioned that Chebyshev's inequality, Hölder type inequality and Minkowski type inequality for Choquet integrals are proved more easily by using the refinements of Jensen type inequality in 2 dimensions. What's more, we provide some examples in the case of the distorted Lebesgue measure to illustrate our results.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
