Hölder and Minkowski type inequalities for pseudo-integral

There are proven generalizations of the Hölder’s and Minkowski’s inequalities for the pseudo-integral. There are considered two cases of the real semiring with pseudo-operations: one, when pseudo-operations are defined by monotone and continuous function g, the second semiring (a, b], sup, ⊙), where ⊙ is generated and the third semiring where both pseudo-operations are idempotent, i.e., ⊕ = sup and ⊙ = inf.