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Journal Article

On Cauchy-Schwarz’s inequality for Choquet-like integrals without the comonotonicity condition

Agahi H., Mesiar Radko

: Soft Computing vol.19, 6 (2015), p. 1627-1634

: Cauchy-Schwarz’s inequality, Choquet expectation, Hölder’s inequality, Monotone probability, Pseudo-analysis, Choquet-like integrals, Sugeno integral

: 10.1007/s00500-014-1578-0

: http://library.utia.cas.cz/separaty/2019/E/mesiar-0506951.pdf

(eng): Cauchy-Schwarz’s inequality is one of the most important inequalities in probability, measure theory and analysis. The problem of finding a sharp inequality of Cauchy–Schwarz 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 Cauchy–Schwarz’s 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 $$g$$g. Another class concerns the Choquet-like integrals based on the operator “$$\sup $$sup” and a pseudo-multiplication $$\otimes $$⊗. When working on the second class of Choquet-like integrals, our results give a new version of Cauchy–Schwarz’s inequality for Sugeno integral without the comonotonicity condition based on the multiplication operator.

: BA

: 10102

2019-01-07 08:39