Initial coefficient bounds for certain new subclasses of bi-univalent functions with bounded boundary rotation

Prathviraj Sharma; Srikandan Sivasubramanian; Nak Eun Cho; Prathviraj Sharma; Srikandan Sivasubramanian; Nak Eun Cho

doi:10.3934/math.20231512

AIMS Mathematics

2023, Volume 8, Issue 12: 29535-29554. doi: 10.3934/math.20231512

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Initial coefficient bounds for certain new subclasses of bi-univalent functions with bounded boundary rotation

1.
Department of Mathematics, University College of Engineering Tindivanam, Anna University, Tindivanam 604001, Tamilnadu, India
2.
Department of Applied Mathematics, Pukyong National University, Busan 48513, Republic of Korea

Received: 18 September 2023 Revised: 19 October 2023 Accepted: 23 October 2023 Published: 31 October 2023
MSC : 30C45, 30C80, 33C50

In the current article, we introduced new subclasses of bi-univalent functions associated with bounded boundary rotation. For these new classes, the authors first obtained two initial coefficient bounds. They also verified the special cases where the familiar Brannan and Clunie's conjecture were satisfied. Furthermore, the famous Fekete-Szegö inequality was obtained for the newly defined subclasses of bi-univalent functions, and some of the results improved the earlier results available in the literature.
- analytic,
- univalent,
- close-to-star,
- close-to-convex,
- bounded boundary rotation,
- coefficient estimate
Citation: Prathviraj Sharma, Srikandan Sivasubramanian, Nak Eun Cho. Initial coefficient bounds for certain new subclasses of bi-univalent functions with bounded boundary rotation[J]. AIMS Mathematics, 2023, 8(12): 29535-29554. doi: 10.3934/math.20231512

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Abstract

In the current article, we introduced new subclasses of bi-univalent functions associated with bounded boundary rotation. For these new classes, the authors first obtained two initial coefficient bounds. They also verified the special cases where the familiar Brannan and Clunie's conjecture were satisfied. Furthermore, the famous Fekete-Szegö inequality was obtained for the newly defined subclasses of bi-univalent functions, and some of the results improved the earlier results available in the literature.

References

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