广西师范大学学报（自然科学版） ›› 2020, Vol. 38 ›› Issue (1): 54-59.doi: 10.16088/j.issn.1001-6600.2020.01.007

• • 上一篇    下一篇

单叶调和函数的一个子类

孙祚晨, 王麒翰, 龙波涌*   

  1. 安徽大学数学科学学院,安徽合肥230601
  • 收稿日期:2018-09-26 出版日期:2020-01-25 发布日期:2020-01-15
  • 通讯作者: 龙波涌(1974—),男(侗族),湖南会同人,安徽大学副教授,博士。E-mail:longboyong@ahu.edu.cn
  • 基金资助:
    国家自然科学基金(11501001);安徽省自然科学基金(1908085MA18),安徽大学科研项目(J01006023, Y01002428)

A Subclass of Harmonic Univalent Functions

SUN Zuochen, WANG Qihan, LONG Boyong*   

  1. School of Mathematical Science, Anhui University, Hefei Anhui 230601, China
  • Received:2018-09-26 Online:2020-01-25 Published:2020-01-15

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摘要： 本文研究一类Salagean型单叶调和函数,得到了这类函数的拟共形性、凸性和卷积性, 改进了相关的结果。

关键词: 调和函数, 拟共形映射, Salagean导数, 卷积, 凸性

Abstract: A class of Salagean-type harmonic univalent functions is investigated. Quasiconformality, convexity and convolution of this class are obtained. Some related results are improved.

Key words: harmonic functions, quasiconformal mappings, Salagean derivative, convolution, convexity

中图分类号: 

  • O174.51
[1] CLUNIE J, SHEIL-SMALL T. Harmonic univalent functions[J].Annales Academiæ Scientiarum Fennicæ Mathematica,1984,9: 3-25.
[2] AL-SHAQSI K, DARUS M, FADIPE-JOSEPH O A. A new subclass of Salagean-type harmonic univalent functions[J].Abstract and Applied Analysis,2010,Art.ID 821531:12.
[3] CHEN S L, PONNUSAMY S, WANG X T. Coefficient estimates and Landau-Blochs constant for planar harmonic mappings[J].Bulletin of the Malaysian Mathematical Sciences Society,2011,34(2): 255-265.
[4] CHEN X D, FANG A N. Harmonicity of the inverse of a harmonicdiffeomorphism[J].Journal of Mathematical Analysis and Applications,2012,389(1): 647-655.
[5] HUANG X Z. Estimates on Bloch constants for planar harmonic mappings[J].Journal of Mathematical Analysis and Applications,2008,337(2): 880-887.
[6] JAHANGIRI J M. Harmonic functions starlike in the unit disk[J].Journal of Mathematical Analysis and Applications,1999,235(2): 470-477.
[7] JAHANGIRI J M. Coecient bounds and univalence criteria for harmonic functionswith negative coeffcients[J].Annales Universitatis Mariae Curie-Skłodowska Sectio A Mathematica,1998,52(2): 57-66.
[8] LI L L, PONNUSAMY S. Solution to an open problem on convolutions of harmonic mappings[J].Complex Variables and Elliptic Equations,2013,58(12): 1647-1653.
[9] LIU M S. Landau’s theorems for biharmonic mappings[J].Complex Variables and Elliptic Equations,2008,53(9): 843-855.
[10]SILVERMAN H, SILVIA E M. Subclasses of harmonic univalent functions[J].New Zealand Journal of Mathematics,1999,28(2): 275-284.
[11]WANG X T, LIANG X Q, ZHANG Y L. Precise coecient estimates for close-to-convex harmonic univalent mappings[J].Journal of Mathematical Analysis and Applications,2001,263(2): 501-509.
[12]WANG Z G, LIU Z H, LI Y C. On the linear combinations of harmonic univalent mappings[J].Journal of Mathematical Analysis and Applications,2013,400(2): 452-459.
[13]ZHU J F. Some estimates for harmonic mappings with given boundary function[J].Journal of Mathematical Analysis and Applications,2014,411(2): 631-638.
[14]SILVERMAN H. Harmonic univalent functions with negative coefficients[J].Journal of Mathematical Analysis and Applications,1998,220(1): 283-289.
[15]SǍLǍGEAN G Ş . Subclasses of univalent functions[C]//Complex Analysis-Fifth Romanian Finish Seminar. Berlin Heidelberg: Springer,1983: 362-372.
[16]JAHANGIRI J M, MURUGUSNDARAMOORTHY G, VIJAKA K. Salagean-type harmonic univalent functions[J]. Southwest Journal of Pure and Applied Mathematics,2002,2: 77-82.
[17]SUBRAMANIAN K G, SUDHARSAN T V, STEPHEN B A, et al. A note on Salagean-type harmonic univalent functions[J].General Mathematics,2008,16(3): 29-40.
[18]KALAJ D, PAVLOVI Ć M. Boundary correspondence under quasiconformal harmonic diffeomorphisms of a half-plane[J].Annales Academiæ Scientiarum Fennicæ Mathematica,2005,30(1): 159-165.
[19]KNEŽEVIĆ M, MATELJEVIĆ M. On the quasi-isometries of harmonic quasiconformal mappings[J].Journal of Mathematical Analysis and Applications,2007,334(1): 404-413.
[20]PAVLOVIĆ M. Boundary correspondence under harmonic quasiconformal homeomorphisms of the unit disk[J].Annales Academiæ Scientiarum Fennicæ Mathematica,2002,27(2): 365-372.
[21]JAHANGIRI J M , SILVERMAN H. Harmonic close-to-convex mappings[J].Journal of Applied Mathematics and Stochastic Analysis,2002,15(1): 23-28.
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