Geometric properties of harmonic functions associated with the symmetric conjecture points and exponential function

Lina Ma; Shuhai Li; Huo Tang; Lina Ma; Shuhai Li; Huo Tang

doi:10.3934/math.2020437

AIMS Mathematics

2020, Volume 5, Issue 6: 6800-6816. doi: 10.3934/math.2020437

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Research article

Geometric properties of harmonic functions associated with the symmetric conjecture points and exponential function

1.
School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, Inner Mongolia, China
2.
Laboratory of Mathematics and Complex Systems, Chifeng University, Chifeng 024000, Inner Mongolia, China

Received: 07 June 2020 Accepted: 24 August 2020 Published: 02 September 2020
MSC : 30C45, 30C65

In this paper, some classes of univalent harmonic functions are introduced by subordination, where the analytic parts of which are exponential starlike (or convex) functions with respect to the symmetric conjecture points. According to the relationships of the analytic part and the co-analytic part, the geometric properties, such as coefficient estimates, distortion theorems, integral expressions, estimates and growth conditions and covering theorem, of the classes are obtained.
- harmonic function,
- exponential function,
- subordination,
- symmetric conjecture point,
- coefficient estimates
Citation: Lina Ma, Shuhai Li, Huo Tang. Geometric properties of harmonic functions associated with the symmetric conjecture points and exponential function[J]. AIMS Mathematics, 2020, 5(6): 6800-6816. doi: 10.3934/math.2020437

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Abstract

In this paper, some classes of univalent harmonic functions are introduced by subordination, where the analytic parts of which are exponential starlike (or convex) functions with respect to the symmetric conjecture points. According to the relationships of the analytic part and the co-analytic part, the geometric properties, such as coefficient estimates, distortion theorems, integral expressions, estimates and growth conditions and covering theorem, of the classes are obtained.

References

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