Coefficient estimates for close-to-convex functions with argument $β$

Details Coefficient estimates for close-to-convex functions with argument $β$ Coefficient estimates for close-to-convex functions with argument $β$

2010-10-27

arxiv.org/abs/1010.5609v1

Mathematics

Complex Variables

Scientific paper

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.

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