A Liapunov type inequality for Sugeno integrals |
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Authors: | Dug Hun Hong |
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Affiliation: | aDepartment of Mathematics, Myongji University, Yongin Kyunggido 449-728, South Korea |
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Abstract: | The classical Liapunov inequality shows an interesting upper bound for the Lebesgue integral of the product of two functions. This paper proposes a Liapunov type inequality for Sugeno integrals. That is, we show that holds for some constant Hs,t,r where 0<t<s<r,f:[0,1]→[0,∞) is a non-increasing concave function, and μ is the Lebesgue measure on R. We also present two interesting classes of functions for which the classical Liapunov type inequality for Sugeno integrals with Hs,t,r=1 holds. Some examples are provided to illustrate the validity of the proposed inequality. |
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Keywords: | Fuzzy measure Sugeno integral Liapunov type inequality |
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