M. Fait, J. Krzyz and J. Zygmunt proved that a strongly starlike function of order α on the unit disk can be extended to a k-quasiconformal mapping with k ≤ sin（απ/2） on the whole complex plane C which fixes the...M. Fait, J. Krzyz and J. Zygmunt proved that a strongly starlike function of order α on the unit disk can be extended to a k-quasiconformal mapping with k ≤ sin（απ/2） on the whole complex plane C which fixes the point at infinity. An open question is whether such a function can be extended to a k-quasiconformal mapping with k 〈α to the whole plane C. In this paper we will give a negative approach to the question.展开更多
基金This research was supported by NNSF of China(Grant No.10231040)NCET(06-0504)
文摘M. Fait, J. Krzyz and J. Zygmunt proved that a strongly starlike function of order α on the unit disk can be extended to a k-quasiconformal mapping with k ≤ sin（απ/2） on the whole complex plane C which fixes the point at infinity. An open question is whether such a function can be extended to a k-quasiconformal mapping with k 〈α to the whole plane C. In this paper we will give a negative approach to the question.
