On Cauchy-Schwarz's inequality for Choquet-like integrals without the comonotonicity condition
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| 024 | 7 | 0 | |a 10.1007/s00500-014-1578-0 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00500-014-1578-0 | ||
| 245 | 0 | 0 | |a On Cauchy-Schwarz's inequality for Choquet-like integrals without the comonotonicity condition |h [Elektronische Daten] |c [Hamzeh Agahi, Radko Mesiar] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2015 | ||
| 690 | 7 | |a Monotone probability |2 nationallicence | |
| 690 | 7 | |a Choquet expectation |2 nationallicence | |
| 690 | 7 | |a Sugeno integral |2 nationallicence | |
| 690 | 7 | |a Choquet-like integrals |2 nationallicence | |
| 690 | 7 | |a Cauchy-Schwarz's inequality |2 nationallicence | |
| 690 | 7 | |a Hölder's inequality |2 nationallicence | |
| 690 | 7 | |a Pseudo-analysis |2 nationallicence | |
| 700 | 1 | |a Agahi |D Hamzeh |u Department of Mathematics, Faculty of Basic Sciences, Babol University of Technology, Babol, Iran |4 aut | |
| 700 | 1 | |a Mesiar |D Radko |u Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, 81368, Bratislava, Slovakia |4 aut | |
| 773 | 0 | |t Soft Computing |d Springer Berlin Heidelberg |g 19/6(2015-06-01), 1627-1634 |x 1432-7643 |q 19:6<1627 |1 2015 |2 19 |o 500 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00500-014-1578-0 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00500-014-1578-0 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Agahi |D Hamzeh |u Department of Mathematics, Faculty of Basic Sciences, Babol University of Technology, Babol, Iran |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Mesiar |D Radko |u Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, 81368, Bratislava, Slovakia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Soft Computing |d Springer Berlin Heidelberg |g 19/6(2015-06-01), 1627-1634 |x 1432-7643 |q 19:6<1627 |1 2015 |2 19 |o 500 | ||