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

Abstract

In this paper, we introduce a new comprehensive subclass ΣB(λ,μ,β) of meromorphic bi-univalent functions in the open unit disk U. We also find the upper bounds for the initial Taylor-Maclaurin coefficients |b0|, |b1| and |b2| for functions in this comprehensive subclass. Moreover, we obtain estimates for the general coefficients |bn|(n≧1) for functions in the subclass ΣB(λ,μ,β) by making use of the Faber polynomial expansion method. The results presented in this paper would generalize and improve several recent works on the subject.

Keywords

• analytic functions
• univalent and bi-univalent functions
• meromorphic bi-univalent functions
• coefficient estimates
• Faber polynomial expansion
• meromorphic bi-Bazilevič functions of order <i>β</i> and type <i>μ</i>