A Liapunov type inequality for Sugeno integrals

被引:16
|
作者
Hong, Dug Hun [1 ]
机构
[1] Myongji Univ, Dept Math, Yongin Kyunggido 449728, South Korea
关键词
Fuzzy measure; Sugeno integral; Liapunov type inequality; HARDY-TYPE INEQUALITY; FUZZY;
D O I
10.1016/j.na.2011.07.046
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 H-s,H-t,H-r ((s) integral(1)(0) f(x)(s)d mu)(r-t) <= ((s) integral(1)(0) f(x)(t)d mu)(r-s) ((s) integral(1)(0) f(x)(r)d mu)(s-t) holds for some constant H-s,H-t,H-r where 0 < t < s < r, f : [0, 1] -> [0,infinity) is a non-increasing concave function, and mu 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 H-s,H-t,H-r = 1 holds. Some examples are provided to illustrate the validity of the proposed inequality. (C) 2011 Elsevier Ltd. All rights reserved.
引用
收藏
页码:7296 / 7303
页数:8
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