A comprehensive subclass of bi-univalent functions defined by a linear combination and satisfying subordination conditions

Hari Mohan Srivastava; Pishtiwan Othman Sabir; Khalid Ibrahim Abdullah; Nafya Hameed Mohammed; Nejmeddine Chorfi; Pshtiwan Othman Mohammed; Hari Mohan Srivastava; Pishtiwan Othman Sabir; Khalid Ibrahim Abdullah; Nafya Hameed Mohammed; Nejmeddine Chorfi; Pshtiwan Othman Mohammed

doi:10.3934/math.20231533

AIMS Mathematics

2023, Volume 8, Issue 12: 29975-29994. doi: 10.3934/math.20231533

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A comprehensive subclass of bi-univalent functions defined by a linear combination and satisfying subordination conditions

1.
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
2.
Section of Mathematics, International Telematic University Uninettuno, Rome I-00186, Italy
3.
Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea
4.
Department of Mathematics, College of Science, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq
5.
Department of Mathematics, College of Basic Education, University of Raparin, Ranya, Kurdistan Region, Iraq
6.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
7.
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq

Received: 09 September 2023 Revised: 28 October 2023 Accepted: 31 October 2023 Published: 06 November 2023
MSC : 26A51, 30C45, 30C50, 30C80

In this article, we derive some estimates for the Taylor-Maclaurin coefficients of functions that belong to a new general subclass $ \Upsilon_\Sigma(\delta, \rho, \tau, n;\varphi) $ of bi-univalent functions in an open unit disk, which is defined by using the Ruscheweyh derivative operator and the principle of differential subordination between holomorphic functions. Our results are more accurate than the previous works and they generalize and improve some outcomes that have been obtained by other researchers. Under certain conditions, the derived bounds are smaller than those in the previous findings. Furthermore, if we specialize the parameters, several repercussions of this generic subclass will be properly obtained.
- holomorphic functions,
- bi-univalent functions,
- coefficient estimates,
- starlike functions,
- convex functions,
- Ruscheweyh derivative,
- subordination
Citation: Hari Mohan Srivastava, Pishtiwan Othman Sabir, Khalid Ibrahim Abdullah, Nafya Hameed Mohammed, Nejmeddine Chorfi, Pshtiwan Othman Mohammed. A comprehensive subclass of bi-univalent functions defined by a linear combination and satisfying subordination conditions[J]. AIMS Mathematics, 2023, 8(12): 29975-29994. doi: 10.3934/math.20231533

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Abstract

In this article, we derive some estimates for the Taylor-Maclaurin coefficients of functions that belong to a new general subclass $ \Upsilon_\Sigma(\delta, \rho, \tau, n;\varphi) $ of bi-univalent functions in an open unit disk, which is defined by using the Ruscheweyh derivative operator and the principle of differential subordination between holomorphic functions. Our results are more accurate than the previous works and they generalize and improve some outcomes that have been obtained by other researchers. Under certain conditions, the derived bounds are smaller than those in the previous findings. Furthermore, if we specialize the parameters, several repercussions of this generic subclass will be properly obtained.

References

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