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 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.