The purpose of this paper is to investigate the Thunsdorff’s inequality for Sugeno integral. By an example, we show that the classical form of this inequality does not hold for Sugeno integral. Then, by reviewing the initial conditions, we prove two main theorems for this inequality. Finally, by checking the special case of the aforementioned Thunsdorff’s inequality, we prove Frank–Pick type inequality for the Sugeno integral and illustrate it by an example.

中文翻译：

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Sugeno 积分的相关 Thunsdorff 型和 Frank-Pick 型不等式

本文的目的是研究 Sugeno 积分的 Thunsdorff 不等式。通过一个例子，我们证明了这个不等式的经典形式不适用于 Sugeno 积分。然后，通过回顾初始条件，我们证明了这个不等式的两个主要定理。最后，通过检验上述 Thunsdorff 不等式的特例，我们证明了 Sugeno 积分的 Frank-Pick 型不等式，并通过实例加以说明。