A Special Family of m-Fold Symmetric Bi-Univalent Functions Satisfying Subordination Condition

Abstract

In this paper, we introduce a special family Mσm(τ,ν,η,φ) of the function family σm of m-fold symmetric bi-univalent functions defined in the open unit disc D and obtain estimates of the first two Taylor–Maclaurin coefficients for functions in the special family. Further, the Fekete–Szegö functional for functions in this special family is also estimated. The results presented in this paper not only generalize and improve some recent works, but also give new results as special cases.