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 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. (C) 2012 Elsevier B.V. All rights reserved.