Faber polynomial coefficients for certain subclasses of analytic and biunivalent functions

Authors: ABDEL MONEIM LASHIN, FATMA ELEMAM

Abstract: In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions defined in the open unit disc. We use the Faber polynomial expansions to find upper bounds for the $n$th$~(n\geq 3)$ Taylor-Maclaurin coefficients $\left\vert a_{n}\right\vert $ of functions belong to these new subclasses with $a_{k}=0$ for $2\leq k\leq n-1$, also we find non-sharp estimates on the first two coefficients $\left\vert a_{2}\right\vert $ and $\left\vert a_{3}\right\vert $. The results, which are presented in this paper, would generalize those in related earlier works of several authors.

Keywords: Faber polynomial, univalent functions, bi-univalent functions, coefficient bounds

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