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Integral representations of bounded starlike functions

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Rønning F.

Annales Polonici Mathematici

1994-1995

tom 60

nr 3

289-297

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.

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1 Annales Polonici Mathematici

1 Rønning F.

1 1995

Wyniki wyszukiwania

Integral representations of bounded starlike functions