Generalizations of the steffensen integral inequality for pseudo-integrals

Abstract

Abstract In this paper, our aim is to prove certain kinds of Steffensen type integral inequalities for the pseudo-integral and the discrete pseudo-integral. The observations concern two cases of the real semiring with pseudo-operations with respect to pseudo-integrals: the first semiring, where pseudo-operations are defined via a monotone and continuous function g, the second semiring, when pseudo-operations are given by an idempotent addition and a generated pseudo-multiplication. Moreover, the discrete pseudo-integral is based on symmetric pseudo-addition and pseudo-multiplication, where the generator g is odd and increasing. In each case, several practical examples are presented to illustrate these results.