CONVEX CLASS OF STARLIKE FUNCTIONS
スポンサーリンク
概要
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Let ＄S＄ denote the class of functions of the form ＄f(z)=z-￥sum_{n=2}^{￥infty}|a_{n}|z^{n}＄ that are analytic and univalent in the unit disk ＄U＄. Let ＄S(￥alpha, ￥beta)＄ and ＄K(￥alpha, ￥beta)＄ denote the subclasses of ＄S＄ consisting respectively, of starlike and close-to-convex functions of order ＄￥alpha(0￥leqq￥alpha<1)＄ and type ＄￥beta(0<￥beta￥leqq 1)＄ . In this Paper, we obtain a relationship between classes ＄S(￥alpha, ￥beta)＄ and ＄K(￥alpha, ￥beta)＄ by defining a subclass ＄B(￥alpha, ￥beta)＄ of ＄K(￥alpha, ￥beta)＄ . Coefficient estimates, distortion and covering theorems are obtained for the class ＄B(￥alpha, ￥beta)＄ . The class ＄B(a, ￥beta)＄ is convex.
- Yokohama City Universityの論文
- 1984-00-00
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