Certain new subclasses of bi-univalent function associated with bounded boundary rotation involving sǎlǎgean derivative

Anandan Murugan; Sheza M. El-Deeb; Mariam Redn Almutiri; Jong-Suk-Ro; Prathviraj Sharma; Srikandan Sivasubramanian; Anandan Murugan; Sheza M. El-Deeb; Mariam Redn Almutiri; Jong-Suk-Ro; Prathviraj Sharma; Srikandan Sivasubramanian

doi:10.3934/math.20241339

AIMS Mathematics

2024, Volume 9, Issue 10: 27577-27592. doi: 10.3934/math.20241339

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Research article

Certain new subclasses of bi-univalent function associated with bounded boundary rotation involving sǎlǎgean derivative

1.
Department of Mathematics, College of Engineering Guindy, Anna University, Chennai 600025, Tamilnadu, India
2.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
3.
School of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea
4.
Department of Intelligent Energy and Industry, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea
5.
Department of Mathematics, University College of Engineering Tindivanam, Anna University, Tindivanam 604001, Tamilnadu, India

Received: 17 July 2024 Revised: 04 September 2024 Accepted: 11 September 2024 Published: 24 September 2024
MSC : Primary 30C45, 33C50, Secondary 30C80

In this article, using the Sǎlǎgean operator, we introduced three new subclasses of bi-univalent functions associated with bounded boundary rotation in open unit disk $ \mathbb{E}. $ For these new classes, we first obtain initial Taylor-Maclaurin's coefficient bounds. Furthermore, the famous Fekete-Szegö inequality was also derived for these new subclass functions. Some improved results, when compared with those available in the literature, are also stated.
- analytic,
- bi-univalent,
- Sǎlǎgean operator,
- bounded boundary rotation,
- convolution,
- coefficient estimates
Citation: Anandan Murugan, Sheza M. El-Deeb, Mariam Redn Almutiri, Jong-Suk-Ro, Prathviraj Sharma, Srikandan Sivasubramanian. Certain new subclasses of bi-univalent function associated with bounded boundary rotation involving sǎlǎgean derivative[J]. AIMS Mathematics, 2024, 9(10): 27577-27592. doi: 10.3934/math.20241339

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Abstract

In this article, using the Sǎlǎgean operator, we introduced three new subclasses of bi-univalent functions associated with bounded boundary rotation in open unit disk $ \mathbb{E}. $ For these new classes, we first obtain initial Taylor-Maclaurin's coefficient bounds. Furthermore, the famous Fekete-Szegö inequality was also derived for these new subclass functions. Some improved results, when compared with those available in the literature, are also stated.

References

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