Abstract
Here we present Hardy type integral inequalities for Choquet integrals. These are very general inequalities involving convex and increasing functions. Initially we collect a rich machinery of results about Choquet integrals needed next, and we prove also results of their own merit such as, Choquet–Hölder’s inequalities for more than two functions and a multivariate Choquet–Fubini’s theorem. The main proving tool here is the property of comonotonicity of functions. We finish with independent estimates on left and right Riemann–Liouville–Choquet fractional integrals.
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Anastassiou, G.A. (2019). Hardy Type Inequalities for Choquet Integrals. In: Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators. Studies in Systems, Decision and Control, vol 190. Springer, Cham. https://doi.org/10.1007/978-3-030-04287-5_5
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DOI: https://doi.org/10.1007/978-3-030-04287-5_5
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