Abstract
A functional equation Σmi=1aiu(φi(z)) = f(z) is considered, where {φi(z)mi=1 are holomorphic functions in a neighborhood of z = 0 with φi(0) = 0 and f(z) is holomorphic in a sector with vertex z = 0. It is shown under some conditions of {φi(z)mi=1, f(z) and {ai}mi=1 that the equation has a formal power series solution that is Borel summable.