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Open AccessArticle

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

School of Mathematics and Statistics, Chifeng University, Chifeng 024000, Inner Mongolia, China
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Mathematics 2019, 7(6), 548; https://doi.org/10.3390/math7060548
Received: 19 May 2019 / Revised: 2 June 2019 / Accepted: 12 June 2019 / Published: 16 June 2019
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2019)
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. View Full-Text
Keywords: harmonic univalent functions; subordination; with symmetric conjecture point; integral expressions; coefficient estimates; distortion harmonic univalent functions; subordination; with symmetric conjecture point; integral expressions; coefficient estimates; distortion
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MDPI and ACS Style

Ma, L.; Li, S.; Niu, X. Some Classes of Harmonic Mapping with a Symmetric Conjecture Point Defined by Subordination. Mathematics 2019, 7, 548. https://doi.org/10.3390/math7060548

AMA Style

Ma L, Li S, Niu X. Some Classes of Harmonic Mapping with a Symmetric Conjecture Point Defined by Subordination. Mathematics. 2019; 7(6):548. https://doi.org/10.3390/math7060548

Chicago/Turabian Style

Ma, Lina; Li, Shuhai; Niu, Xiaomeng. 2019. "Some Classes of Harmonic Mapping with a Symmetric Conjecture Point Defined by Subordination" Mathematics 7, no. 6: 548. https://doi.org/10.3390/math7060548

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