Turkish Journal of Mathematics
Abstract
This paper is concerned with the problem of estimating $ a_4-a_2a_3 $, where $a_k$ are the coefficients of a given close-to-convex function. The bounds of this expression for various classes of analytic functions have been applied to estimate the third Hankel determinant $H_3(1)$. The results for two subclasses of the class $\mathcal{C}$ of all close-to-convex functions are sharp. This bound is equal to 2. It is conjectured that this number is also the exact bound of $ a_4-a_2a_3 $ for the whole class $\mathcal{C}$.
DOI
10.3906/mat-1711-36
Keywords
Close-to-convex functions, coefficient problem
First Page
2809
Last Page
2818
Recommended Citation
WIECLAW, KATARZYNA TRABKA and ZAPRAWA, PAWEL
(2018)
"On the coefficient problem for close-to-convex functions,"
Turkish Journal of Mathematics: Vol. 42:
No.
5, Article 56.
https://doi.org/10.3906/mat-1711-36
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss5/56
