On nonvanishing solutions of a class of functional equations

摘要

We study some properties of the solutions of a class of functional equations. For example, we prove that if w(z) is a function analytic in the closed unit disc {z z less than or equal to 1} such that w(0) = 0, 0 < epsilon < 1, andw'(z)+'epsilonw(z) = 1, z = 1,then w(z) not equal 0 if z = 1.