P\'olya-Knopp and Hardy-Knopp type inequalities for Sugeno integral

Abstract

In this paper, we investigate the P\'olya-Knopp type inequality for Sugeno integrals in two cases. In the first case, we suppose that the inner integral is the standard Riemann integral and the remaining two integrals are of Sugeno type. In the second case, all involved integrals are Sugeno integral. We present several examples illustrating the validity of our theorems. Finally, we prove a Hardy-Knopp type inequality for Sugeno integral.