Coefficient Estimates of a New Subclass of r-Fold Symmetric Bi-Univalent Functions Involving Ruscheweyh Derivative

Authors

Nihad H. Shehab, Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, IraqFollow
Abdul Rahman S. Juma, Department of Mathematics, College of Education for Pure Sciences, University of Anbar, Anbar, IraqFollow
Maslina Darus, Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor D. Ehsan, MalaysiaFollow

Abstract

In this work, the authors introduce and study a new subclass ofM^h,u_Σr(γ,η,κ,λ), which is r-fold bi-univalent functions in open-unit disk 𝔄. Using the Rushwaya derivative operator, the study investigates the properties and behavior of an analytically generalized r-fold symmetric two-monovalent function in the open-unit disk 𝔄. The analysis calculates the Taylor-Maclarin coefficients |a_r+1| and |a_2r+1|, which represent one of its key terms these estimates M^h,u_Σr(γ,η,κ,λ). Subclass of functions important for understanding analytical and geometric behavior they provide valuable insights into the development of these concepts and their relationship to the geometric properties of the functions. Furthermore, research goes beyond coefficient estimates to examine the significance of results. By analyzing this expression, the study highlights the circumstantial importance of the M^h,u_Σr(γ,η,κ,λ) subclass plant. The importance of this new subclass is essentially its ability to add special information to specific operator users, as well as the inclusion of multiple values to increase its flexibility and robustness. Furthermore, by linking us to prior research in the field, the study strengthens the theoretical framework and deepens our understanding of these activities, thus contributing to extensive knowledge in this area.

Keywords

Analytic functions, Bi-Univalent functions, r-Fold Symmetric Function, Ruscheweyh derivative operator, Univalent functions

Subject Area

Mathematics

Article Type

Article

First Page

3479

Last Page

3492

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite this Article

Shehab, Nihad H.; Juma, Abdul Rahman S.; and Darus, Maslina (2025) "Coefficient Estimates of a New Subclass of r-Fold Symmetric Bi-Univalent Functions Involving Ruscheweyh Derivative," Baghdad Science Journal: Vol. 22: Iss. 10, Article 24.
DOI: https://doi.org/10.21123/2411-7986.5096