Several inequalities for the pan-integral

Several inequalities for the pan-integral are investigated. It is shown that the Chebyshev inequality holds for an arbitrary subadditive measure if and only if the integrands f, g are comonotone. Thus, we provide a new characterization for nonnegative comonotone functions. It is also shown that the...

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Bibliographic Details
Published in:Information sciences 2016-12, Vol.372, p.625-633
Main Authors: Zhao, Yuchen, Yan, Tingsu, Ouyang, Yao
Format: Article
Language:English
Subjects:
Chebyshev approximation
Chebyshev inequality
Comonotonicity
Hölder inequality
Inequalities
Integrals
Minkowski inequality
Pan-integral
Subadditive measure
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Summary:Several inequalities for the pan-integral are investigated. It is shown that the Chebyshev inequality holds for an arbitrary subadditive measure if and only if the integrands f, g are comonotone. Thus, we provide a new characterization for nonnegative comonotone functions. It is also shown that the Hölder and Minkowski inequalities for the pan-integral hold if the monotone measure μ is subadditive. Since the pan-integral coincides with the concave integral when μ is subadditive, our results can also be applied to the concave integral.
ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2016.08.067