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

Authors:
Mirjana ŠTrboja;Tatjana Grbi;Ivana ŠTajner-Papuga;Gabrijela Gruji;Slavica Medi
Affiliations:
Department of Mathematics and Informatics, University of Novi Sad, Serbia;Faculty of Technical Sciences, University of Novi Sad, Serbia;Department of Mathematics and Informatics, University of Novi Sad, Serbia;Faculty of Technical Sciences, University of Novi Sad, Serbia;Faculty of Technical Sciences, University of Novi Sad, Serbia
Venue:
Fuzzy Sets and Systems
Year:
2013

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Abstract

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.