Chinese Quarterly Journal of Mathematics ›› 2009, Vol. 24 ›› Issue (2): 310-316.

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A Remark on the Generalized Roper-Suffridge Extension Operator for Spirallike Mappings of Type β and Order α

  

  1. 1. School of Mathematics and Computation Science, Zhanjiang Normal University2. Institute of Mathematics, Henan University3. College of Mathematics and Information Science, Henan University
  • Received:2006-03-24 Online:2009-06-30 Published:2023-08-11
  • About author: LIU Xiao-song(1968-), male, native of Shaoyang, Hunan, an associate professor of Zhanjiang Normal University, engages in function theory of SCV; FENG Shu-xia(1975-), female, native of Yuanyang, Henan, an associate professor of Henan University, engages in function theory of SCV.
  • Supported by:
     Supported by the National Natural Science Foundation of China(10626015, 10571044); Supported by Guangdong Natural Science Foundation(06301315); Supported by the doctoral foundation of Zhanjiang Normal University(Z0420);

Abstract: Suppose f is a spirallike function of type β and order α on the unit disk D. Let ... , where 1 ≤ p1 ≤ 2,pj ≥1,j = 2,··· ,n, are real numbers. In this paper, we will prove that ···, preserves spirallikeness of type βand order α on Ωn,p1,p2,···,pn.

Key words: spirallike mapping of type β and order α, starlike mapping of order α, generalized Roper-Suffridge extension operator

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