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Fekete-Szegő functional for non-Bazilevič functions. (English) Zbl 1017.30012
Let 0<λ<1. The authors consider the class of holomorphic functions f(z)=z+a 2 z 2 + in the unit 𝒰:={|z|<1} with the property that f ' (z)(z/f(z)) 1+λ has positive real part for all z𝒰. For those functions they give sharp estimates for |a 2 | as well as for the Fekete–Szegö functional |a 3 -μa 2 2 |, where μ is an arbitrary complex number.
MSC:
30C50Coefficient problems for univalent and multivalent functions
30C45Special classes of univalent and multivalent functions