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Some Classes of Harmonic Mapping with a Symmetric Conjecture Point Defined by Subordination

Author

Listed:
  • Lina Ma

    (School of Mathematics and Statistics, Chifeng University, Chifeng 024000, Inner Mongolia, China)

  • Shuhai Li

    (School of Mathematics and Statistics, Chifeng University, Chifeng 024000, Inner Mongolia, China)

  • Xiaomeng Niu

    (School of Mathematics and Statistics, Chifeng University, Chifeng 024000, Inner Mongolia, China)

Abstract

In the paper, we introduce some subclasses of harmonic mapping, the analytic part of which is related to general starlike (or convex) functions with a symmetric conjecture point defined by subordination. Using the conditions satisfied by the analytic part, we obtain the integral expressions, the coefficient estimates, distortion estimates and the growth estimates of the co-analytic part g , and Jacobian estimates, the growth estimates and covering theorem of the harmonic function f . Through the above research, the geometric properties of the classes are obtained. In particular, we draw figures of extremum functions to better reflect the geometric properties of the classes. For the first time, we introduce and obtain the properties of harmonic univalent functions with respect to symmetric conjugate points. The conclusion of this paper extends the original research.

Suggested Citation

  • Lina Ma & Shuhai Li & Xiaomeng Niu, 2019. "Some Classes of Harmonic Mapping with a Symmetric Conjecture Point Defined by Subordination," Mathematics, MDPI, vol. 7(6), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:548-:d:240329
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    References listed on IDEAS

    as
    1. Yaşar Polatoğlu & Metın Bolcal & Arzu Şen, 2003. "Two-point distortion theorems for certain families of analytic functions in the unit disc," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-11, January.
    2. Mengkun Zhu & Xinzhong Huang, 2015. "The Distortion Theorems for Harmonic Mappings with Analytic Parts Convex or Starlike Functions of Order," Journal of Mathematics, Hindawi, vol. 2015, pages 1-6, October.
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