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Zbl 1134.30310
Janteng, Aini; Halim, Suzeini Abdul; Darus, Maslina
Coefficient inequality for a function whose derivative has a positive real part.
(English)
[J] JIPAM, J. Inequal. Pure Appl. Math. 7, No. 2, Paper No. 50, 5 p., electronic only (2006). ISSN 1443-5756/e

Summary: Let $\cal R$ denote the subclass of normalised analytic univalent functions $f$ defined by $f(z)=z+\sum^\infty_{n=2}a_nz^n$ which satisfy $$\mathrm{Re}\{f'(z)\}>0$$ where $z\in{\cal D}=\{z: |z|<1\}$. The object of the present paper is to introduce the functional $|a_2a_4-a^2_3|$. For $f\in\cal R$, we give sharp upper bound on $|a_2a_4-a^2_3|$.
MSC 2000:
*30C45 Special classes of univalent and multivalent functions
30C50 Coefficient problems for univalent and multivalent functions

Keywords: Fekete-Szegö functional; Hankel determinant; convex and starlike functions; positive real functions

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