Publications de l’Institut Mathématique, Nouvelle Série Vol. 101[115], pp. 143–149 (2017) 

A NOTE ON THE FEKETE–SZEGÖ PROBLEM FOR CLOSETOCONVEX FUNCTIONS WITH RESPECT TO CONVEX FUNCTIONSBogumiła Kowalczyk, Adam Lecko, H. M. SrivastavaDepartment of Complex Analysis, University of Warmia and Mazury, Olsztyn, Poland; Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada; China Medical University, Taichung, Taiwan, Republic of ChinaAbstract: We discuss the sharpness of the bound of the Fekete–Szegö functional for closetoconvex functions with respect to convex functions. We also briefly consider other related developments involving the Fekete–Szegö functional ${a}_{3}\lambda {a}_{2}^{2}$ ($0\le \lambda \le 1$) as well as the corresponding Hankel determinant for the Taylor–Maclaurin coefficients ${\left\{{a}_{n}\right\}}_{n\in \mathbb{N}\setminus \left\{1\right\}}$ of normalized univalent functions in the open unit disk $\mathbb{D}$, $\mathbb{N}$ being the set of positive integers. Keywords: analytic functions; convex functions; Fekete–Szegö problem; Hankel determinant; TaylorMaclaurin coefficients; closetoconvex functions with respect to a convex function; Carathéodory class; Schwarz functions Classification (MSC2000): 30C45 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 24 Apr 2017. This page was last modified: 11 May 2017.
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