I have to talk into a paper of mine about a new proposed operator: do you think it is of any use to talk about it within the introduction? My problem is that, by doing so, maybe a reader/reviewer could arise more problems than the ones he could motivate by reading the whole description later on the paper. On the other hand an example of such operator within the introduction helps the reader/reviewer to better understand the problem this new operator tries to solve. Another problem is that, if the example is too simple, then he could think that more difficult tasks could not be solved by this specific operator. Thanks in advance!
The introduction should highlight whatever you think is most important and most likely to catch the interest of your readers. It should be a summary/overview of your results.
If your goal is to define a new operator, definitely say so in the introduction. If you need several motivating examples, say so in the introduction. If the examples are too involved to summarize, tell the reader from what area these motivating examples come.
In this paper we define a new operator X with several applications for the study of A, B, C in the context of [area]. In §2 "Motivating Examples" we give several motivating examples, including [this well-known example]. In particular, we find that X generalizes operator Y that Smith and Taylor defined in [2,3] to study Rubber Ducks (see [2,3,10–12]).
The Introduction should serve for "introducing" the problem you claim to solve. Generally, you might want to start with a very short background which brings you to talk about the problem definition and the proposed solution. In your case, the proposed operator seems to be the solution you are proposing. Therefore, i would personally say only few rather general information on the operator and leave the technical discussion to other sessions in the paper. I hope i answered to your doubts. BR, Alessio.