Geodesic
Integral representations of bounded starlike functions
Annales Polonici Mathematici, Tome 60 (1994) no. 3, pp. 289-297

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For α ≥ 0 let $ℱ_α$ denote the class of functions defined for |z| 1 by integrating $1/(1-xz)^α$ if α > 0, and log(1/(1-xz)) if α = 0, against a complex measure on |x| = 1. We study families of starlike functions where zf'(z)/f(z) ranges over a parabola with given focus and vertex. We prove a number of properties of these functions, among others that they are bounded and that they belong to $ℱ_0$. In general, it is only known that bounded starlike functions belong to $ℱ_α$ for α > 0.
DOI : 10.4064/ap-60-3-289-297
Keywords: Cauchy-Stieltjes integrals, starlike functions

Frode Rønning 1

1 
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Frode Rønning. Integral representations of bounded starlike functions. Annales Polonici Mathematici, Tome 60 (1994) no. 3, pp. 289-297. doi: 10.4064/ap-60-3-289-297

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