Geodesic
On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application
Kybernetika, Tome 52 (2016) no. 3, pp. 329-347 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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].
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].
DOI : 10.14736/kyb-2016-3-0329
Classification : 26E50, 28E10
Keywords: seminormed fuzzy integral; semicopula; monotone measure; Minkowski's inequality; Hölder's inequality; convergence in mean 
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     title = {On the {Minkowski-H\"older} type inequalities for generalized {Sugeno} integrals with an application},
     journal = {Kybernetika},
     pages = {329--347},
     year = {2016},
     volume = {52},
     number = {3},
     doi = {10.14736/kyb-2016-3-0329},
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     zbl = {06644298},
     language = {en},
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Boczek, Michał; Kaluszka, Marek. On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application. Kybernetika, Tome 52 (2016) no. 3, pp. 329-347. doi: 10.14736/kyb-2016-3-0329

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