Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (3): 722-731.doi: 10.1016/S0252-9602(17)30033-4

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FEKETE AND SZEGÖ INEQUALITY FOR A SUBCLASS OF STARLIKE MAPPINGS OF ORDER α ON THE BOUNDED STARLIKE CIRCULAR DOMAIN IN Cn

Taishun LIU1, Qinghua XU2   

  1. 1. Department of Mathematics, Huzhou University, Huzhou 313000, China;
    2. School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China
  • Received:2016-01-04 Online:2017-06-25 Published:2017-06-25
  • Supported by:

    This work was supported by NNSF of China (11471111,11561030 and 11261022),the Jiangxi Provincial Natural Science Foundation of China (20152ACB20002,20161BAB201019),and Natural Science Foundation of Department of Education of Jiangxi Province,China (GJJ150301).

Abstract:

In this article, first, we establish the Fekete and Szegö inequality for an interesting subclass of biholomorphic functions in the open unit disk U. Second, we generalize this result to the bounded starlike circular domain in Cn. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.

Key words: Fekete-Szegöproblem, starlike mappings of order α, bounded starlike circular domain

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