Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (3): 769-777.doi: 10.1016/S0252-9602(18)30782-3

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GROWTH AND DISTORTION THEOREMS FOR ALMOST STARLIKE MAPPINGS OF COMPLEX ORDER λ

Xiaofei ZHANG1, Jin LU2, Xiaofei LI1   

  1. 1. School of Mathematics and Statistics, Pingdingshan University, Pingdingshan 467000, China;
    2. Department of Mathematics, Huzhou University, Zhejiang 313000, China
  • Received:2016-12-14 Revised:2017-08-22 Online:2018-06-25 Published:2018-06-25
  • Contact: Jin LU E-mail:luking@zjhu.edu.cn
  • Supported by:

    Supported by the National Natural Science Foundation of China (11501198, 11701307), the Key Scientific Research Projects in Universities of Henan Province (16B110010), the Zhejiang Natural Science Foundation of China (LY16A010012), the Doctoral Foundation of Pingdingshan University (PXY-BSQD-2015005), and the Foster Foundation of Pingdingshan University (PXYPYJJ2016007).

Abstract:

In this article, the sharp growth theorem for almost starlike mappings of complex order λ is given firstly. Secondly, distortion theorem along a unit direction is also established as the application of the growth theorem. In particular, using our results can reduce to some well-known results.

Key words: Distortion theorem, convex mapping, Schwarz lemma at the boundary

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