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

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A NOTE ON THE FEKETE–SZEGÖ PROBLEM FOR CLOSE-TO-CONVEX FUNCTIONS WITH RESPECT TO CONVEX FUNCTIONS

Bogumiła Kowalczyk, Adam Lecko, H. M. Srivastava

Department 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 China

Abstract: We discuss the sharpness of the bound of the Fekete–Szegö functional for close-to-convex functions with respect to convex functions. We also briefly consider other related developments involving the Fekete–Szegö functional |a 3 -λa 2 2 | (0λ1) as well as the corresponding Hankel determinant for the Taylor–Maclaurin coefficients {a n } n{1} of normalized univalent functions in the open unit disk 𝔻, being the set of positive integers.

Keywords: analytic functions; convex functions; Fekete–Szegö problem; Hankel determinant; Taylor-Maclaurin coefficients; close-to-convex functions with respect to a convex function; Carathéodory class; Schwarz functions

Classification (MSC2000): 30C45

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