Bi-univalent functions subordinated to a three leaf function induced by multiplicative calculus

G. Murugusundaramoorthy; K. Vijaya; K. R. Karthikeyan; Sheza M. El-Deeb; Jong-Suk Ro; G. Murugusundaramoorthy; K. Vijaya; K. R. Karthikeyan; Sheza M. El-Deeb; Jong-Suk Ro

doi:10.3934/math.20241313

AIMS Mathematics

2024, Volume 9, Issue 10: 26983-26999. doi: 10.3934/math.20241313

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Research article

Bi-univalent functions subordinated to a three leaf function induced by multiplicative calculus

1.
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT), Vellore 632014, India
2.
Department of Applied Mathematics and Science, College of Engineering, National University of Science & Technology, P. O. Box 2322, CPO Seeb 111, Al Hail, Muscat, Oman
3.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
4.
School of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea
5.
Department of Intelligent Energy and Industry, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea

Received: 29 June 2024 Revised: 29 August 2024 Accepted: 09 September 2024 Published: 18 September 2024
MSC : 30C45

Our aim was to develop a new class of bi starlike functions by utilizing the concept of subordination, driven by the idea of multiplicative calculus, specifically multiplicative derivatives. Several restrictions were imposed, which were indeed strict constraints, because we have tried to work within the current framework or the design of analytic functions. To make the study more versatile, we redefined our new class of function with Miller-Ross Poisson distribution (MRPD), in order to increase the study's adaptability. We derived the first coefficient estimates and Fekete-Szegő inequalities for functions in this new class. To demonstrate the characteristics, we have provided a few examples.
- analytic function,
- bi-univalent function,
- convolution,
- Miller-Ross function,
- multiplicative calculus,
- subordination,
- Poisson distribution
Citation: G. Murugusundaramoorthy, K. Vijaya, K. R. Karthikeyan, Sheza M. El-Deeb, Jong-Suk Ro. Bi-univalent functions subordinated to a three leaf function induced by multiplicative calculus[J]. AIMS Mathematics, 2024, 9(10): 26983-26999. doi: 10.3934/math.20241313

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Abstract

Our aim was to develop a new class of bi starlike functions by utilizing the concept of subordination, driven by the idea of multiplicative calculus, specifically multiplicative derivatives. Several restrictions were imposed, which were indeed strict constraints, because we have tried to work within the current framework or the design of analytic functions. To make the study more versatile, we redefined our new class of function with Miller-Ross Poisson distribution (MRPD), in order to increase the study's adaptability. We derived the first coefficient estimates and Fekete-Szegő inequalities for functions in this new class. To demonstrate the characteristics, we have provided a few examples.

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