Schwarzian derivative and Landau's theorem for logharmonic mappings

被引：18
|
作者：
Mao, Zh [1 ]
Ponnusamy, S. [2 ]
Wang, X. [1 ]
机构：
[1] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China
[2] Indian Inst Technol, Dept Math, Madras 600036, Tamil Nadu, India
来源：
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2013年 / 58卷 / 08期
关键词：
Schwarzian derivative; Schwarz' lemma; Landau's theorem; logharmonic mapping; PLANAR HARMONIC-MAPPINGS; BLOCH CONSTANTS;
D O I：
10.1080/17476933.2011.629725
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The main aim of this article is twofold. First, we introduce the Schwarzian derivative for logharmonic mappings F, and obtain several necessary and sufficient conditions for to be analytic. Second, we establish Schwarz' lemma for logharmonic mappings, through which two versions of the Landau's theorem for these functions are obtained.
引用
收藏
页码：1093 / 1107
页数：15
相关论文
共 50 条
  • [41] Stable geometric properties of pluriharmonic and biholomorphic mappings, and Landau–Bloch’s theorem
    Shaolin Chen
    Saminathan Ponnusamy
    Xiantao Wang
    Monatshefte für Mathematik, 2015, 177 : 33 - 51
  • [42] LANDAU'S THEOREM AND MARDEN CONSTANT FOR HARMONIC v-BLOCH MAPPINGS
    Chen, Sh.
    Ponnusamy, S.
    Wang, X.
    BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2011, 84 (01) : 19 - 32
  • [43] Logharmonic mappings on linearly connected domains
    El Hajj, Layan
    ANALYSIS AND MATHEMATICAL PHYSICS, 2019, 9 (02) : 829 - 837
  • [44] One pointed univalent logharmonic mappings
    Abdulhadi, Z
    Hengartner, W
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 203 (02) : 333 - 351
  • [45] Schwarzian derivative, integral means, and the affine and linear invariant families of biharmonic mappings
    Ponnusamy, S.
    Qiao, J.
    Wang, X.
    APPLIED MATHEMATICS AND COMPUTATION, 2010, 216 (12) : 3468 - 3479
  • [46] SCHOTTKY-LANDAU TYPE THEOREM FOR HOLOMORPHIC MAPPINGS
    Meng, Fan-Ning
    Mori, Seiki
    Yuan, Wenjun
    HOUSTON JOURNAL OF MATHEMATICS, 2016, 42 (01): : 101 - 121
  • [47] LOGHARMONIC MAPPINGS WITH TYPICALLY REAL ANALYTIC COMPONENTS
    AbdulHadi, Zayid
    Alarifi, Najla M.
    Ali, Rosihan M.
    BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2018, 55 (06) : 1783 - 1789
  • [48] Pre-Schwarzian and Schwarzian Derivatives of Harmonic Mappings
    Hernandez, Rodrigo
    Martin, Maria J.
    JOURNAL OF GEOMETRIC ANALYSIS, 2015, 25 (01) : 64 - 91
  • [49] Stable geometric properties of pluriharmonic and biholomorphic mappings, and Landau-Bloch's theorem
    Chen, Shaolin
    Ponnusamy, Saminathan
    Wang, Xiantao
    MONATSHEFTE FUR MATHEMATIK, 2015, 177 (01): : 33 - 51
  • [50] Strengthening of Landau's Theorem for Holomorphic Self-Mappings of a Disk with Fixed Points
    Solodov, A. P.
    MATHEMATICAL NOTES, 2020, 108 (3-4) : 626 - 628
12345