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

Lina Ma, Shuhai Li and Xiaomeng Niu
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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

Mathematics, 2019, vol. 7, issue 6, 1-18

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.

Keywords: harmonic univalent functions; subordination; with symmetric conjecture point; integral expressions; coefficient estimates; distortion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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