On the coefficient problem for close-to-convex functions

Authors : KATARZYNA TRABKA WIECLAW, PAWEL ZAPRAWA

Pages : 2809-2818

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Publication Date : 0000-00-00

Article Type : Research Paper

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 $H_3insert ignore into journalissuearticles values(1);$. 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