Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate

Abstract

In this paper, we use the Faber polynomial expansion to find upper bounds for |an| (n ≥ 3) coefficients of functions belong to classes $\begin{array}{} H_{q}^{\Sigma}(\lambda,h),\, ST_{q}^{\Sigma}(\alpha,h)\,\text{ and} \,\,M_{q}^{\Sigma}(\alpha,h) \end{array}$ which are defined by quasi-subordinations in the open unit disk 𝕌. Further, we generalize some of the previously published results.

Coefficient Bounds for Certain Classes of Analytic Functions Associated with Faber Polynomial

“…If we take β = 0 in Theorem 3, then we have the results which were given by Zireh et al [51] when ϕ(z) = 1.…”

Coeficient estimates for a subclass of meromorphic bi-univalent functions defined by subordination

“…But the interest on coefficient estimates of the meromorphic univalent functions keep on by many researchers, see for example, [18,19,25,26]. Several authors by using Faber polynomial expansions obtained coefficient estimates |a n | for classes meromorphic bi-univalent functions and bi-univalent functions, see for example [10,12,13,14,15,16,17,28,27]. First we recall some definitions and lemmas that used in this work.…”

Coefficients of a Comprehensive Subclass of Meromorphic Bi-Univalent Functions Associated with the Faber Polynomial Expansion

“…For a brief history and interesting examples of functions in the class σ B , see the pioneering work [1]. In fact, this widely-cited work by Srivastava et al [1] actually revived the study of analytic and bi-univalent functions in recent years, and it has also led to a flood of papers on the subject by (for example) Srivastava et al [2][3][4][5][6][7][8][9][10][11][12][13][14] and by others [15,16].…”