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Article

Boczek, Michał ; Kaluszka, Marek
On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application. (English). Kybernetika, vol. 52 (2016), issue 3, pp. 329-347
MSC: 26E50, 28E10 | MR 3532510 | Zbl 06644298 | DOI: 10.14736/kyb-2016-3-0329
Keywords:
seminormed fuzzy integral; semicopula; monotone measure; Minkowski's inequality; Hölder's inequality; convergence in mean
Summary:
In this paper, we use a new method to obtain the necessary and sufficient condition guaranteeing the validity of the Minkowski-Hölder type inequality for the generalized upper Sugeno integral in the case of functions belonging to a wider class than the comonotone functions. As a by-product, we show that the Minkowski type inequality for seminormed fuzzy integral presented by Daraby and Ghadimi [11] is not true. Next, we study the Minkowski-Hölder inequality for the lower Sugeno integral and the class of $\mu$-subadditive functions introduced in [20]. The results are applied to derive new metrics on the space of measurable functions in the setting of nonadditive measure theory. We also give a partial answer to the open problem 2.22 posed in [5].
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