Jensen and Chebyshev inequalities for pseudo-integrals of set-valued functions

Jensen and Chebyshev inequalities for pseudo-integrals of set-valued functions

Set-valued functions are an important mathematical notion and play a crucial role in several practical areas. At the same time, pseudo-analysis as a background allows extension of some classical mathematical notions to the forms that are highly applicable in some nonstandard situations. This paper f...

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Bibliographic Details
Published in:Fuzzy sets and systems Vol. 222; pp. 18 - 32
Main Authors: ANBtrboja, Mirjana, GrbiA, Tatjana, ANBtajner-Papuga, Ivana, GrujiA, Gabrijela, MediA, Slavica
Format: Journal Article
Language:English
Published: Elsevier B.V 01-07-2013
Subjects:
Chebyshev approximation
Chebyshev-type inequality
Functions (mathematics)
Fuzzy set theory
Inequalities
Integrals
Jensen-type inequality
Mathematical analysis
Pseudo-integral
Pseudo-operations
Set-valued functions
Chebyshev-type inequality
Pseudo-operations
Set-valued functions
Jensen-type inequality
Pseudo-integral
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Summary:Set-valued functions are an important mathematical notion and play a crucial role in several practical areas. At the same time, pseudo-analysis as a background allows extension of some classical mathematical notions to the forms that are highly applicable in some nonstandard situations. This paper focuses on pseudo-integration of set-valued functions, which is generalization of Aumann's research, and corresponding extensions of the Jensen and Chebyshev integral inequalities to the set-valued case. Since the integral inequalities in question are widely used in various aspects of mathematics, the main motivation for the presented research lies in the possibility of expanding the applicability of these inequalities by combining the properties of set-valued functions with pseudo-analysis.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2012.07.011