On the implicit function theorem

The implicit function is a basic theorem of mathematical analysis and it has a major importance in many mathematical problems. This theorem has many formulations, see [5]. Every category of functions has its own special version of implicit function theorem and there are particular versions adapted to Banach spaces, algebraic geometry and to functions that are not even smooth. The aim of this article is to state and to proof a version of analytic implicit function theorem for functions of two variables. Then we will give an application.