PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 52(66), pp. 1826 (1992) 

On the FeketeSzego theorem for closetoconvex functionsA. Chonweerayoot, D.K. Thomas and W. UpakarnitikasetDepartment of Mathematics and Computer Science, University of Wales, Swansea SA2 8PP, Wales, U.K. (Thomas) and Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand (A. Chonweerayoot and W. Upakarnitikaset)Abstract: Let $K(\beta)$ be the class of normalised closetoconvex functions with order $\beta\ge0$, defined in the unit disc $D$ by $$ \left\arg e^{i\lambda}\dfrac{zf'(z)}{g(z)}\right\le\dfrac{\pi\beta}{2}, $$ for $\lambda<\pi/2$ and $g$ starlike in $D$. For $f\in K(\beta)$ with $f(z)=z+a_2z^2+a_3z^3+\cdots$ and $z\in D$, sharp bounds are given for $a_3\mu a_2^2$ for real $\mu$. Classification (MSC2000): 30C45 Full text of the article:
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