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The Fekete-Szegö coefficient functional for transforms of analytic functions. (English) Zbl 1193.30006

Summary: Sharp bounds for the Fekete-Szegö coefficient functional associated with the \(k\)-th root transform \(\big[f(z^k)\big]^{1/k}\) of normalized analytic functions \(f(z)\) defined on the open unit disk in the complex plane are derived. A similar problem is investigated for functions \(z/f(z)\) when \(f\) belongs to a certain class of functions.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
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