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.

Certain Class of Bi-Univalent Functions Defined by Sălăgean q-Difference Operator Related with Involution Numbers

“…Also by taking q → 1 − we state various subclasses of Σ and state results analogues to Theorem 1 and 3. This paper can motivate many researchers to extend this idea to another classes of biunivalent functions [37], Sakaguchi-type functions [38] (other classes of functions cited in this article) and further second Hankel determinant results for function class Σ, as discussed in [39].…”

Applications of Certain Conic Domains to a Subclass of q-Starlike Functions Associated with the Janowski Functions

“…The importance of the results demonstrated in this paper is obvious from the fact that these results would generalize and extend various previously known results derived in many earlier works. Moreover, with a view to motivating and encouraging further researches on the subject of our investigation, we have chosen to cite several recently-published articles (see, for example, [45][46][47][48]) on a wide variety of developments in Geometric Function Theory of Complex Analysis.…”

New family of bi-univalent functions with respect to symmetric conjugate points associated with Borel distribution

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