On the existence and uniqueness of locally analytic invertible solutions of a system of nonlinear functional equations

In the present research work, a set of necessary and sufficient conditions is derived, under which a rather broad class of nonlinear functional equations admits a unique locally analytic and invertible solution which can be easily computed with the aid of a symbolic software package. The main results naturally reproduce the solution of the linear problem, where the system of functional equations to be solved becomes equivalent to a Lyapunov matrix equation.