Choquet integral analytic inequalities

Abstract

Based on an amazing result of Sugeno [15], we are able to transfer classic analytic integral inequalities to Choquet integral setting. We give Choquet integral inequalities of the following types: fractional-Polya, Ostrowski, fractional Ostrowski, Hermite-Hadamard, Simpson and Iyengar. We provide several examples for the involved distorted Lebesgue measure.