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

Departamento de Matemática

Universidad de Tarapacá

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

48 Citas (Scopus)

Resumen

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, ∞).

Idioma original	Inglés
Páginas (desde-hasta)	178-183
Número de páginas	6
Publicación	Applied Mathematics and Computation
Volumen	204
N.º	1
DOI	https://doi.org/10.1016/j.amc.2008.06.027
Estado	Publicada - 1 oct. 2008

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title = "A Hardy-type inequality for fuzzy integrals",

abstract = "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, ∞).",

keywords = "Fuzzy measure, Hardy's inequality, Sugeno integral",

author = "H. Rom{\'a}n-Flores and A. Flores-Franuli{\v c} and Y. Chalco-Cano",

year = "2008",

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AU - Román-Flores, H.

AU - Flores-Franulič, A.

AU - Chalco-Cano, Y.

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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

U2 - 10.1016/j.amc.2008.06.027

DO - 10.1016/j.amc.2008.06.027

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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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