Turkish Journal of Mathematics
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.
DOI
10.3906/mat-2002-7
Keywords
Faber polynomial, univalent functions, bi-univalent functions, coefficient bounds
First Page
1345
Last Page
1361
Recommended Citation
LASHIN, A. M, & ELEMAM, F (2020). Faber polynomial coefficients for certain subclasses of analytic and biunivalent functions. Turkish Journal of Mathematics 44 (4): 1345-1361. https://doi.org/10.3906/mat-2002-7
