Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (6): 1582-1591.

• Articles • Previous Articles     Next Articles

The Roper-Suffridge Extension Operator in Complex Banach Space

 ZU Juan   

  1. College of Mathematics and Computational Science, Shenzhen University, Guangdong Shenzhen 518060
  • Received:2008-01-18 Revised:2009-10-11 Online:2010-12-25 Published:2010-12-25
  • Supported by:

    国家自然科学基金(10571121)和广东省自然科学基金(5010509)资助

Abstract:

In this paper, the author extends the Roper-Suffridge operator to some domains in complex Banach space, and it is proved that certain extended Roper-Suffridge operator preserves spirallikeness of type α on the relevant domain, while another extended Roper-Suffridge operator preserves starlikeness of order α on the unit ball in a complex Banach space. Some results of Liu T S , Liu X S and Feng S X in Hilbert space are extended to Banach spaces.

Key words: Roper-Suffridge operator, Spirallike mapping of type α, Starlike mapping of order α, Complex Banach space

CLC Number: 

  • 32A30
Trendmd