Analytic solutions of an iterative functional equation

摘要

This paper is concerned with the functional equation f (p (z) + bf (z)) = h (z) for f. By constructing a convergent power series solution of an auxiliary equation of the form analytic solutions of the form g(β~2z) - p(g(βz)) = bh(g(z)), analytic solutions of the form f(z) = {g(βg~(-1)(z)) - p(z)}/b for the original equation are obtained.