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 mathemat- ical 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.