Say you have an idea and you can't find any paper or book that explicitly states that idea. You don't know for sure if you're right in assuming that you came up first with that idea so you decide to publish it. What are the consequences if you're wrong and the idea has already been published. Do the reviewers point that out for you before the paper gets published? Is your career over because of that?
To be more specific, I have an idea for constructing iterative formulas for solving systems of nonlinear equations for any convergence rate. I also have an elegant proof for that. The problem is that I have found just one article that explicitly states that idea just for functions of one variable, but doesn't expand on it.( just one paragraph and then continues with something else)