On the Coefficent Estimate of Univalent Functions whose Ranges are Extended Polygons

This paper concerns with the coefficie3nt estimate of univalent functions whose ranges are extended polygons with interior angles λ_kπ, where -2≦λ_k≦2 (k=1, 2,-,m). Conditions for range of functions are made weaker than ones which were trested in two previous notes [1] and [2], but the same is true of previous conclusion on the estimate of coefficients in Taylor's expansion of univalent functions which map conformally the interior of unit circle onto above extended regions. As application, we give a new proof of a Reade's theorem.