Related Thunsdorff type and Frank–Pick type inequalities for Sugeno integral

Abstract 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.