I want to add non-cited references to bibliography for two reasons.
Sometimes, it is not clear whether I referred to it or not. Clearly, not only citing a statement is a citation, but also citing an idea is a citation. But if I didn't cite the ideas and if another idea comes across my mind, sometimes I can not sure my idea is inspired by the references or not. In that case, I want to add the references to bibliography.
There are some references I didn't cite but it would be useful for the readers.
May I feel free to add non-cited reference to bibliography?
Addition: Maybe I had to clarify I am in Mathematics field, and many authors add the references to bibliography as a "reference", not as a "cited writing". If I cited anything, then I will definitely notify the readers the citation specifically. However, is it not allowed to add some papers or books to bibliography that I just referred to?