doiSerbia

A note on the Fekete-Szegö problem for close-to-convex functions with respect to convex functions

Kowalczyk Bogumiła (University of Warmia and Mazury, Faculty of Mathematics and Computer Science, Department of Complex Analysis, Olsztyn, Poland)
Lecko Adam (University of Warmia and Mazury, Faculty of Mathematics and Computer Science, Department of Complex Analysis, Olsztyn, Poland)
Srivastava H.M. (University of Victoria, Department of Mathematics and Statistics, Victoria, Canada + China Medical University, Taichung, Taiwan, Republic of China)

We discuss the sharpness of the bound of the Fekete-Szego functional for close-to-convex functions with respect to convex functions. We also briefly consider other related developments involving the Fekete-Szego functional |a3 −λa22| (0 ≤ λ ≤ 1) as well as the corresponding Hankel determinant for the Taylor-Maclaurin coefficients {an}nN\{1} of normalized univalent functions in the open unit disk D, N being the set of positive integers.

Keywords: analytic functions, convex functions, Fekete-Szego problem, Hankel determinant, Taylor-Maclaurin coefficients, close-to-convex functions with respect to a convex function, Caratheodory class, Schwarz functions