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Zbl 1117.30009
Elin, Mark
Covering and distortion theorems for spirallike functions with respect to a boundary point. (English)
[J] Int. J. Pure Appl. Math. 28, No. 3, 387-400 (2006). ISSN 1311-8080

The author obtains certain distortion results for spirallike functions with respect to a boundary point. In Theorem 2.1 the author deduces an integral representation for functions in the class $G(\mu,\beta)$ which consists of $\mu$-spirallike functions of order $\beta$ with respect to a boundary point. In Corollary 2.4, the author proves that if $f\in G(\mu,\beta)$ then $f(z)/(1-z)^\mu\prec 1/(1-z)^{\mu(1-\beta)}$. In the third section of this paper, there are deduced some estimates for $f$ and $f'$, and in the last section it is obtained a covering result for the class $G(\mu,\beta)$.
[Gabriela Kohr (Cluj-Napoca)]

MSC 2000:: *30C45 Special classes of univalent and multivalent functions

Keywords: convex domain; covering theorem; distortion result; spirallike function; subordination; univalent function

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