Fekete-Szegö problem for close-to-convex functions with respect to a certain convex function dependent on a real parameter

• Published in: Frontiers of mathematics in China Vol. 11; no. 6; pp. 1471 - 1500
• Main Authors: CHO, Nak Eun, KOWALCZYK, Bogumi a, LECKO, Adam
• Format: Journal Article
• Language: English
• Published: Beijing Higher Education Press 01.12.2016; Springer Nature B.V
• Subjects: close-to-convex functions; close-to-convex functions with argumentδ; close-to-convex functions with respect to a convex function; Convex analysis; Fekete-Szegö problem; Functions (mathematics); functions of bounded turning; Mathematical analysis; Mathematics; Mathematics and Statistics; Parameters; Research Article; Studies; functions of bounded turning; 30C45; close-to-convex functions with argument; Fekete-Szegö problem; close-to-convex functions; close-to-convex functions with respect to a convex function
• ISSN: 1673-3452; 1673-3576
• DOI: 10.1007/s11464-015-0510-y

Given α ∈[0 , 1] , let h α ( z) := z/(1 − αz) , z ∈ D := { z ∈ C : | z | <1} . An analytic standardly normalized function f in D is called close-to-convex with respect to h α if there exists δ ∈ ( − π/2 , π/2) such that Re{e i δ zf′( z) /h α ( z)} >0 , z ∈ D . For the class C ( h α ) of all close-to-convex functions with respect to h α , the Fekete-Szegö problem is studied.