Generalization of the Lyapunov type inequality for pseudo-integrals

We prove two kinds of Lyapunov type inequalities for pseudo-integrals. One discusses pseudo-integrals where pseudo-operations are given by a monotone and continuous function g. The other one focuses on the pseudo-integrals based on a semiring 0,1,sup,⊙, where the pseudo-multiplication ⊙ is generated. Some examples are given to illustrate the validity of these inequalities.