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On a class of starlike functions defined in a halfplane

G. Dimkov; J. Stankiewicz; Z. Stankiewicz — 1991

Annales Polonici Mathematici

Let D = z: Re z < 0 and let S*(D) be the class of univalent functions normalized by the conditions $l i m_{D ∋ z \to \infty} (f (z) - z) = a$ , a a finite complex number, 0 ∉ f(D), and mapping D onto a domain f(D) starlike with respect to the exterior point w = 0. Some estimates for |f(z)| in the class S*(D) are derived. An integral formula for f is also given.

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