Determining the Coefficient Bounds for a Subclass of k-Fold Symmetric Bi-Univalent Functions

Abstract

This article focuses on presenting estimates of coefficient for certain subclass of h-fold symmetric bi-univalent functions. Bi-univalent functions have significant importance in various areas of mathematics, including complex analysis and geometric function theory. The study of h-fold symmetric bi-univalent functions involves understanding the symmetry of these functions, which is critical in various applications such as image processing and biometric authentication. This article provides estimates of coefficients that play a crucial role in the study of these functions and provides a foundation for further research in this field. Our analysis yielded additional outcomes, including the limits for the first coefficients |d_(h+1) | and |d_(2h+1) |, which are included in the remaining findings. Moreover, the study presents specific and noteworthy improvements in the results for the related classes. The results presented in this paper can contribute to the advancement of our understanding of the properties of h-fold symmetric bi-univalent functions and their applications.