Local solutions of the generalized Dhombres functional equation in a neighbourhood of infinity*

Abstract

We study the generalized Dhombres functional equation in the complex domain, we investigate solutions in a neighbourhood of infinity. After some transformations a characterization of those solutions which have a complex number different from zero or infinity as value is given. Moreover the convergence of the solutions and solutions represented as infinite product are figured out.

Keywords

• generalized dhombres equation
• iterative equation