Generalizations of Some Inequalities for Sugino Integrals

In this paper, we express and prove Bushell-Okrasiaski, Hardy and Minkowski type inequalities for two classes of pseudo-integrals. One of them, classes with pseudo-integrals where pseudo-operations are defined via a monotone and continuous generator function. The other one concerns the pseudo-integrals based on a semiring with an idempotent addition and a pseudo-multiplication generator. Those are important inequalities from both mathematical and application points of view. The established results are based on the classical Bushell-Okrasiaski, Hardy and Minkowski's inequalities for integrals. Also, some examples and applications are presented.