A Liapunov type inequality for Sugeno integrals Original Research Article

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 View the MathML sourceHs,t,r((S)∫01f(x)sdμ)r−t≤((S)∫01f(x)tdμ)r−s((S)∫01f(x)rdμ)s−t Turn MathJax on holds for some constant Hs,t,rHs,t,r where 0