Coefficient estimates for special subclasses of k-fold symmetric bi-univalent functions

Abstract

In the present paper, we consider two new subclasses N Σ k (µ, α, τ ) and N Σ k (µ, β, τ ) of Σ k consisting of analytic and k-fold symmetric bi-univalent functions defined in the open unit disc U = {z : z ∈ C and |z| < 1}. For functions belonging to the two classes introduced here, we derive their normalized forms. Furthermore, we find estimates of the initial coefficients |a k+1 | and |a 2k+1 | for these functions. Several related classes are also considered and connections to previously known results are made.

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