SHARP ESTIMATES OF QUASI-CONVEX MAPPINGS OF TYPE B AND ORDER α

doi:10.1007/s10473-019-0506-x

Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (5): 1265-1276.doi: 10.1007/s10473-019-0506-x

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SHARP ESTIMATES OF QUASI-CONVEX MAPPINGS OF TYPE B AND ORDER α

Mingsheng LIU¹, Fen WU¹, Yan YANG²

1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China;
2. School of Mathematics(Zhuhai), Sun Yat-Sen University, Zhuhai 519080, China

Received:2018-02-27 Revised:2019-01-21 Online:2019-10-25 Published:2019-11-11
Contact: Mingsheng LIU E-mail:liumsh65@163.com
Supported by:
This research was supported by Guangdong Natural Science Foundation (2018A030313508) and Science and Technology Program of Guangzhou, China (201804010171).

Abstract

Abstract: In this paper, we first establish several sharp inequalities of homogeneous expansion for biholomorphic quasi-convex mappings of type B and order α on the unit ball E in a complex Banach space X by applying the method and technique of complex analysis. Then, as the application of these sharp inequalities, we derive the sharp estimate of third homogeneous expansions for the above mappings defined on the unit polydisk Uⁿ in Cⁿ.

Key words: quasi-convex mappings of type B and order α, inequalities of homogeneous expansions, the sharp estimate of third homogeneous expansions

CLC Number:

30C45

Mingsheng LIU, Fen WU, Yan YANG. SHARP ESTIMATES OF QUASI-CONVEX MAPPINGS OF TYPE B AND ORDER α[J].Acta mathematica scientia,Series B, 2019, 39(5): 1265-1276.

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SHARP ESTIMATES OF QUASI-CONVEX MAPPINGS OF TYPE B AND ORDER α

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