Jensen type inequality for the bipolar pseudo-integrals

The main purpose of this paper is to establish conditions under which the Jensen type inequality for the discrete bipolar pseudo-integral is valid. Besides, we extend investigations of the properties of the bipolar pseudo-integral. The observations concern the discrete bipolar pseudo-integrals based on the following three canonical cases of two binary symmetric operations: in the first case, they are generated by an odd, strictly increasing and continuous function, in the remaining two cases a symmetric-addition is the symmetric maximum, while in the second case the corresponding pseudo-multiplication is a non-idempotent operation, and in the third case it is the symmetric minimum.