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Covering and distortion theorems for spirallike functions with respect to a boundary point. (English) Zbl 1117.30009
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(μ,β) which consists of μ-spirallike functions of order β with respect to a boundary point. In Corollary 2.4, the author proves that if fG(μ,β) then f(z)/(1-z) μ 1/(1-z) μ(1-β) . 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(μ,β).
30C45Special classes of univalent and multivalent functions