A Hardy-type inequality for fuzzy integrals

H. Román-Flores; A. Flores-Franulič; Y. Chalco-Cano

doi:10.1016/j.amc.2008.06.027

A Hardy-type inequality for fuzzy integrals

H. Román-Flores
, A. Flores-Franulič
, Y. Chalco-Cano

Department of Mathematics

Universidad de Tarapacá

Research output: Contribution to journal › Article › peer-review

48 Scopus citations

Abstract

In this paper, we prove a Hardy-type inequality for fuzzy integrals. More precisely, we show thatfenced({cauchy integral}₀¹ f^p (x) d x)^{frac(1, p + 1)} ≥ {cauchy integral}₀¹ fenced(frac(F, x))^p d x,where p ≥ 1, f : [0, 1] → [0, ∞) is an integrable function and F (x) = {cauchy integral}₀^x f (t) d t. An analogous inequality is also obtained on the interval [0, ∞).

Original language	English
Pages (from-to)	178-183
Number of pages	6
Journal	Applied Mathematics and Computation
Volume	204
Issue number	1
DOIs	https://doi.org/10.1016/j.amc.2008.06.027
State	Published - 1 Oct 2008

Keywords

Fuzzy measure
Hardy's inequality
Sugeno integral

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AU - Román-Flores, H.

AU - Flores-Franulič, A.

AU - Chalco-Cano, Y.

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Y1 - 2008/10/1

N2 - In this paper, we prove a Hardy-type inequality for fuzzy integrals. More precisely, we show thatfenced({cauchy integral}01 fp (x) d x)frac(1, p + 1) ≥ {cauchy integral}01 fenced(frac(F, x))p d x,where p ≥ 1, f : [0, 1] → [0, ∞) is an integrable function and F (x) = {cauchy integral}0x f (t) d t. An analogous inequality is also obtained on the interval [0, ∞).

AB - In this paper, we prove a Hardy-type inequality for fuzzy integrals. More precisely, we show thatfenced({cauchy integral}01 fp (x) d x)frac(1, p + 1) ≥ {cauchy integral}01 fenced(frac(F, x))p d x,where p ≥ 1, f : [0, 1] → [0, ∞) is an integrable function and F (x) = {cauchy integral}0x f (t) d t. An analogous inequality is also obtained on the interval [0, ∞).

KW - Fuzzy measure

KW - Hardy's inequality

KW - Sugeno integral

UR - https://www.scopus.com/pages/publications/52049114422

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DO - 10.1016/j.amc.2008.06.027

M3 - Article

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VL - 204

SP - 178

EP - 183

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 1

ER -

A Hardy-type inequality for fuzzy integrals

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