Kaliyappan Vijaya, Gangadharan Murugusundaramoorthy, Sa’ud Al-Sa’di, Bi-univalent functions associated with involution numbers based on Sălăgean-Erdély-Kober operator, Vol. 2025 (2025), No. 13, pp. 1-15

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DOI: 10.23952/jnfa.2025.13

Received December 8, 2024; Accepted April 11, 2025; Published May 6, 2025

Abstract. In this paper, we propose two new subclasses of bi-univalent functions defined in the open unit disk and denoted by $\Omega$ , and relate them to the concept of generalized telephone numbers. These subclasses utilize the Sălăgean-Erdély-Kober operator. Furthermore, we examine the initial Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$ and derived Fekete-Szegö inequalities for the functions that belongs to these new subclasses. Additionally, we introduce several other new subclasses of $\Omega$ based on Sălăgean-Erdély-Kober operator, which have not been previously explored in connection with telephone numbers. Some corollaries are also presented.

How to Cite this Article:
K. Vijaya, G. Murugusundaramoorthy, S. Al-Sa’di, Bi-univalent functions associated with involution numbers based on Sălăgean-Erdély-Kober operator, J. Nonlinear Funct. Anal. 2025 (2025) 13.