- Turkish Journal of Mathematics
- Vol: 42 Issue: 5
- On the coefficient problem for close-to-convex functions
On the coefficient problem for close-to-convex functions
Authors : Katarzyna Trabka Wieclaw, Pawel Zaprawa
Pages : 2809-2818
View : 6 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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 $\mathcal{C}$.Keywords : Close-to-convex functions, coefficient problem