Faber Polynomial Coefficients Estimates of Bi-univalent Functions Associated with Generalized Salagean q-Differential Operator

Year 2019, Volume: 7 Issue: 1, 25 - 32, 15.04.2019

Sibel Yalçın Shahid Khan Saqib Hussain

Abstract

In this paper, we introduce a new subclass of analytic and bi-univalent functions by using generalized Salagean $q$-differential operator in open unit disc $E=\left \{ z:z\in \mathbb{C} \text{ and }\left \vert z\right \vert <1\right \} $. By using Faber polynomial expansions and $q-$analysis to find a general coefficient bounds $|a_{n}|,$ for $n\geq 3,$ of class of bi-subordinate functions, also find initial coefficients bounds$.$ We also highlight some known consequences of our main results.

Keywords

Bi-univalent function, Faber polynomial expansions, Generalized Salagean q-Differential Operator

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