A sharp Hardy-type inequality of Sugeno integrals

This paper improves on previous work presenting a Hardy-type inequality for Sugeno integrals. Indeed, we show that for (S)∫Df(x)dx⩽1,(S)∫Df(x)pdx1p+1⩾(S)∫Df(x)dxpp+1⩾(S)∫DF(x)xpdx,where p ⩾ 1, f : D → [0, ∞) is an integrable function on D⊂R and F(x)=(S)∫0xf(t)dt. As a consequence, a Hardy-type inequality for Sugeno integral obtained by Román-Flores et al. [2] follows immediately. General case is also treated.