Affiliation:
1. School of Engineering Management Nanjing University Nanjing P. R. China
2. School of Software Engineering Jinling Institute of Technology Nanjing P. R. China
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.
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