Coefficient estimates for close-to-convex functions with argument $\beta$

Abstract

This paper deals with coefficient estimates for close-to-convex functions with argument $\beta$ ($-\pi /2<\beta <\pi /2$). By using Herglotz representation formula, sharp bounds of coefficients are obtained. In particluar, we solve the problem posed by A. W. Goodman and E. B. Saff in $\cite{GS}$. Finally some complicted computations yield the explicit estimate of the third coefficient.

arXiv commentThis paper has been withdrawn by the author. There is no good reason to keep it since the author found a crucial sign error in equation 1