PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)Vol. 52(66), pp. 18--26 (1992)
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PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 52(66), pp. 18--26 (1992) |
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On the Fekete-Szego theorem for close-to-convex 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 close-to-convex 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:
Electronic fulltext finalized on: 2 Nov 2001. This page was last modified: 16 Nov 2001.
© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
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