A Liapunov type inequality for Sugeno integrals

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 Hs,t,r((S)∫01f(x)sdμ)r−t≤((S)∫01f(x)tdμ)r−s((S)∫01f(x)rdμ)s−t holds for some constant Hs,t,rHs,t,r where 0