Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions

Abstract

‎In this paper‎, ‎we introduce and investigate a subclass‎ of analytic and bi-univalent functions which both $f(z)$ and $f^{-1}(z)$ are m-fold symmetric in the open unit disk U‎. Furthermore‎, ‎we find upper bounds for the initial coefficients $|a_{m‎ + ‎1}|$ and $|a_{2m‎ + ‎1}|$ for functions in this subclass‎. ‎The results presented in this paper would generalize and improve some recent works‎.

Coefficient Bounds and Fekete-Szegӧ Problem for a New Subclasses of Holomorphic Bi-Univalent Functions Defined by Horadam polynomials

“…In the year 2010, Srivastava et al [10] refreshed the study of various classes of bi-univalent functions. Moreover, many penmans explored bounds for different subclasses of bi-univalent functions (see, for example [3,4,8,11,12] [6])…”