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Inequalities of Hölder and Minkowski type for pseudo-integrals with respect to interval-valued \(\oplus\)-measures. (English) Zbl 1368.26024
Summary: In the present paper, the Hölder and Minkowski type of inequality for the pseudo-integral of a real-valued function with respect to the interval-valued pseudo-additive measure is proven. Two cases of semirings are considered. In the first case, pseudo-operations (pseudo-addition and pseudo-multiplication) are set by a strictly monotone continuous function. In the second case, the pseudo-addition is the idempotent operation sup, and pseudo-multiplication is specified by a strictly monotone continuous function, as in the first case. Trivial and nontrivial examples of interval-valued pseudo-additive measures are provided, as well as Hölder and Minkowski type of inequalities with respect to those measures.

26D15 Inequalities for sums, series and integrals
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