Fekete–Szegö Functional Problem for a Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions

Abstract

In the current work, we introduce a special family of the function family of analytic and m-fold symmetric bi-univalent functions and obtain estimates of the Taylor–Maclaurin coefficients |dm+1| and |d2m+1| for functions in the special family. For δ a real number, Fekete–Szegö functional |d2m+1−δdm+12| for functions in the special family is also estimated. We indicate several cases of the defined family and connections to existing results are also discussed.

Keywords

• bi-univalent functions
• coefficient estimates
• Fekete–Szegö functional
• m-fold symmetric bi-univalent functions