Taiwanese Journal of Mathematics

ON SOME SUFFICIENT CONDITIONS FOR STARLIKENESS OF ORDER $\alpha$ IN $C^n$

Ming-Sheng Liu and Yu-Can Zhu

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Abstract

In this paper, we obtain some new sufficient conditions for starlikeness of order $\alpha$ of biholomorphic mappings on the unit ball in $C^n$ or a complex Hilbert space $X$ by using differential inequalities. We also obtain a distortion theorem and a covering theorem. As their special case, we obtain some sufficient conditions for starlikeness of order $\alpha$ of analytic functions on the unit disc in the complex plane $C$, which generalize some results of P. T. Mocanu and G. Oros.

Article information

Source
Taiwanese J. Math., Volume 10, Number 5 (2006), 1169-1182.

Dates
First available in Project Euclid: 20 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500557296

Digital Object Identifier
doi:10.11650/twjm/1500557296

Mathematical Reviews number (MathSciNet)
MR2253372

Subjects
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

Keywords
locally biholomorphic mapping starlike mapping covering theorem

Citation

Liu, Ming-Sheng; Zhu, Yu-Can. ON SOME SUFFICIENT CONDITIONS FOR STARLIKENESS OF ORDER $\alpha$ IN $C^n$. Taiwanese J. Math. 10 (2006), no. 5, 1169--1182. doi:10.11650/twjm/1500557296. https://projecteuclid.org/euclid.twjm/1500557296


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References

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