A Hardy-type inequality for fuzzy integrals

摘要

In this paper, we prove a Hardy-type inequality for fuzzy integrals. More precisely, we show that⨍⨍⨍01fp(x)dx1p+1⩾⨍01Fxpdx,where p⩾1, f:[0,1]→[0,∞) is an integrable function and ⨍F(x)=⨍0xf(t)dt. An analogous inequality is also obtained on the interval [0,∞).