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.
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