Dmitri Goloubentsev, Evgeny Lakshtanov and Vladimir Piterbarg explain in mathematical terms, and demonstrate using a simple example, how the automatic implicit function theorem, a special version of ...

The paper presents a variant of implicit function theorem, as a corollary of existence theorem for solutions of a first order system of partial differential equations. This results is then extend to ...

The main goal of the paper is to obtain explicit integral representations of implicit functions whose existence is guaranteed by the implicit function theory. We derive the mentioned representation ...