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On Cauchy-Schwarz’s inequality for Choquet-like integrals without the comonotonicity condition
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SYSNO ASEP 0506951 Document Type J - Journal Article R&D Document Type The record was not marked in the RIV Subsidiary J Článek ve WOS Title On Cauchy-Schwarz’s inequality for Choquet-like integrals without the comonotonicity condition Author(s) Agahi, H. (IR)
Mesiar, Radko (UTIA-B) RID, ORCIDNumber of authors 2 Source Title Soft Computing. - : Springer - ISSN 1432-7643
Roč. 19, č. 6 (2015), s. 1627-1634Number of pages 8 s. Publication form Print - P Language eng - English Country DE - Germany Keywords Cauchy-Schwarz’s inequality ; Choquet expectation ; Hölder’s inequality ; Monotone probability ; Pseudo-analysis ; Choquet-like integrals ; Sugeno integral Subject RIV BA - General Mathematics OECD category Applied mathematics Institutional support UTIA-B - RVO:67985556 UT WOS 000354500300014 EID SCOPUS 84939997651 DOI 10.1007/s00500-014-1578-0 Annotation 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2020
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