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, K. T, & ZAPRAWA, P (2018). On the coefficient problem for close-to-convex functions. Turkish Journal of Mathematics 42 (5): 2809-2818. https://doi.org/10.3906/mat-1711-36
