Glasnik Matematicki, Vol. 37, No.1 (2002), 89-92.
KOEBE DOMAIN OF STARLIKE FUNCTIONS OF COMPLEX
ORDER WITH MONTEL NORMALIZATION
Yasar Polatoglu, Metin Bolcal and Arzu Sen
Department of Mathematics, Faculty of Science, University of
Kultur, Turkey
e-mail: m.bolcal@iku.edu.tr
Abstract. Let S*(1-b),
(b ≠ 0
complex) denote
the class of functions f(z) = z +
a2z2 + ... analytic in
D = {z : |z| < 1} which satisfies for
z = eiθ
∈ D,
f(z) / z
≠ 0 in D,
and
Re[1 + 1/b(z f'(z) / f(z)
- 1)] > 0.
The aim of this paper is to give the Koebe domain of the above mentioned class.
2000 Mathematics Subject Classification.
30C45.
Key words and phrases. Univalent functions, starlike
functions, starlike functions of comlex order, Montel normalization,
Koebe domain.
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