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.

中文翻译：

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伪积分和伪可加测度的 Wirtinger 积分不等式

本文的主要目的是展示伪积分的 Wirtinger 型不等式。我们关注基于以下三种规范情况的伪积分：在第一种情况下，具有伪运算的实半环由严格单调连续函数 g 生成；在第二种情况下，伪运算包括伪乘法和幂算术加法。在最后一种情况下，⊕-measures 是区间值。给出了例子来说明这些等式。