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Zbl 1132.30007
Choi, Jae Ho; Kim, Yong Chan; Sugawa, Toshiyuki
A general approach to the Fekete-Szegö problem.
(English)
[J] J. Math. Soc. Japan 59, No. 3, 707-727 (2007). ISSN 0025-5645; ISSN 1881-1167; ISSN 1881-2333/e

The study offers a new method to solve the Fekete-Szegö problem for classes of close-to-convex functions defined in terms of subordination. The essence of this problem is concerned with inequalities for the coefficient functional $$\Lambda_\mu(f)= a_3-\mu a^2_2={1\over 6}\biggl(f'''(0)- {3\mu\over 2} [f''(0)]^2\biggr)$$ which corresponds to subclasses of normalized univalent functions in the unit disk, that is $f(z)= z+ a_2z^2+ a_3z^3+\cdots+ \mu\in[0, 1]$. The obtained results are applied to the class of strongly close-to-convex functions.
[Witold Pedrycz (Edmonton)]
MSC 2000:
*30C45 Special classes of univalent and multivalent functions
30C50 Coefficient problems for univalent and multivalent functions

Keywords: univalent function; subordination; coefficient bound

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