On CauchySchwarzs inequality for Choquet-like integrals without the comonotonicity condition
Cauchy-Schwarzs inequality is one of the most important inequalities in probability, measure theory and analysis. The problem of finding a sharp inequality of CauchySchwarz type for Sugeno integral without the comonotonicity condition based on the multiplication operator has led to a challenging and an interesting subject for researchers. In this paper, we give a CauchySchwarzs inequality without the comonotonicity condition based on pseudo-analysis for two classes of Choquet-like integrals as generalizations of Choquet integral and Sugeno integral. In the first class, pseudo-operations are defined by a continuous strictly increasing function \(g\). Another class concerns the Choquet-like integrals based on the operator \(\sup \) and a pseudo-multiplication \(\otimes \). When working on the second class of Choquet-like integrals, our results give a new version of CauchySchwarzs inequality for Sugeno integral without the comonotonicity condition based on the multiplication operator.
cauchyschwarzs inequality choquet-like integrals sugeno integral pseudo-analysis monotone probability choquet expectation hlders inequality