On Cauchy–Schwarz’s inequality for Choquet-like integrals without the comonotonicity condition View Full Text


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Article Info

DATE

2015-06

AUTHORS

Hamzeh Agahi, Radko Mesiar

ABSTRACT

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. Another class concerns the Choquet-like integrals based on the operator “sup” and a pseudo-multiplication ⊗. 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. More... »

PAGES

1627-1634

References to SciGraph publications

  • 2000. Triangular Norms in NONE
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    http://scigraph.springernature.com/pub.10.1007/s00500-014-1578-0

    DOI

    http://dx.doi.org/10.1007/s00500-014-1578-0

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