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Wirtinger integral inequalities for pseudo-integrals and pseudo-additive measure

Jing Guo, Xianjun Zhu

Abstract: The main purpose of this paper is to show Wirtinger type inequalities for the pseudo-integral. We are concerned with pseudo-integrals based on the following three canonical cases: in the first case, the real semiring with pseudo-operation is generated by a strictly monotone continuous function g; in the second case, the pseudo-operations include a pseudo-multiplication and a power arithmetic addition; in the last case, ⊕-measures are interval-valued. Examples are given to illustrate these equalities.
Keywords: 03E72 / 28E10 / 26E50 / 26D15 / Pseudo-operations / Pseudo-integral / Interval-valued measure / Pseudo-addition / Pseudo-multiplication / Wirtinger inequality

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