THE GENERALIZED ROPER-SUFFRIDGE OPERATOR ON THE UNIT BALL IN COMPLEX BANACH AND HILBERT SPACES

doi:10.1016/S0252-9602(17)30109-1

Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (6): 1817-1829.doi: 10.1016/S0252-9602(17)30109-1

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THE GENERALIZED ROPER-SUFFRIDGE OPERATOR ON THE UNIT BALL IN COMPLEX BANACH AND HILBERT SPACES

Yanyan CUI^1,2, Chaojun WANG², Hao LIU³

1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, China;
2. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;
3. Institute of Contemporary Mathematics, Henan University, Kaifeng 475001, China

Received:2016-06-13 Revised:2016-11-20 Online:2017-12-25 Published:2017-12-25
Supported by:
This work is supported by NSF of China (11271359), Science and Technology Research Projects of Henan Provincial Education Department (17A110041), Youth Fund Projects of Zhoukou Normal University (zknuB3201608).

Abstract

Abstract:

In this paper, we extend the Roper-Suffridge extension operator in complex Banach space, and prove that the extended Roper-Suffridge operators preserve the properties of the subclasses of spirallike mappings on the unit ball in complex Banach spaces. Thereby, we promote the conclusions to the cases in complex Hilbert spaces. The conclusions provide new approaches to construct these subclasses of spirallike mappings in several complex variables.

Key words: spirallike mappings, starlike mappings, Roper-Suffridge operator

Yanyan CUI, Chaojun WANG, Hao LIU. THE GENERALIZED ROPER-SUFFRIDGE OPERATOR ON THE UNIT BALL IN COMPLEX BANACH AND HILBERT SPACES[J].Acta mathematica scientia,Series B, 2017, 37(6): 1817-1829.

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References

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THE GENERALIZED ROPER-SUFFRIDGE OPERATOR ON THE UNIT BALL IN COMPLEX BANACH AND HILBERT SPACES

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