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, ABDEL MONEIM and ELEMAM, FATMA
(2020)
"Faber polynomial coefficients for certain subclasses of analytic and biunivalent functions,"
Turkish Journal of Mathematics: Vol. 44:
No.
4, Article 19.
https://doi.org/10.3906/mat-2002-7
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss4/19
