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- Title
On Cauchy-Schwarz's inequality for Choquet-like integrals without the comonotonicity condition.
- Authors
Agahi, Hamzeh; Mesiar, Radko
- 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 $$\otimes $$ . 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.
- Subjects
SCHWARZ inequality; CHOQUET theory; INTEGRALS; MONOTONIC functions; MULTIPLICATION; OPERATOR algebras
- Publication
Soft Computing - A Fusion of Foundations, Methodologies & Applications, 2015, Vol 19, Issue 6, p1627
- ISSN
1432-7643
- Publication type
Article
- DOI
10.1007/s00500-014-1578-0