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Research Article | Open Access

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

Anandan Murugan1, Sheza M. El-Deeb2, Mariam Redn Almutiri2,  Jong-Suk-Ro3,4( ), Prathviraj Sharma5, Srikandan Sivasubramanian5
Department of Mathematics, College of Engineering Guindy, Anna University, Chennai 600025, Tamilnadu, India
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
School of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea
Department of Intelligent Energy and Industry, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea
Department of Mathematics, University College of Engineering Tindivanam, Anna University, Tindivanam 604001, Tamilnadu, India
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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 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.

Keywords

analyticbi-univalentSǎlǎgean operatorbounded boundary rotationconvolutioncoefficient estimates
CLC number: Primary 30C45, 33C50, Secondary 30C80

References

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AIMS Mathematics
Volume 9 Issue 10,
October 2024
Pages 27577-27592
DOI: 10.3934/math.20241339

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Cite this article:
Murugan A, El-Deeb SM, Almutiri MR, et al. Certain new subclasses of bi-univalent function associated with bounded boundary rotation involving sǎlǎgean derivative. AIMS Mathematics, 2024, 9(10): 27577-27592. https://doi.org/10.3934/math.20241339

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Received: 17 July 2024
Revised: 04 September 2024
Accepted: 11 September 2024
Published: 15 October 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)