On the Fekete–Szegö Type Functionals for Close-to-Convex Functions
Mechanical Engineering Faculty, Lublin University of Technology, ul. Nadbystrzycka 36, 20-618 Lublin, Poland
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Symmetry 2019, 11(12), 1497; https://doi.org/10.3390/sym11121497
Received: 28 October 2019 / Revised: 29 November 2019 / Accepted: 7 December 2019 / Published: 10 December 2019
In this paper, we consider two functionals of the Fekete–Szegö type and for a real number and for an analytic function , . This type of research was initiated by Hayami and Owa in 2010. They obtained results for functions satisfying one of the conditions Re or Re , . Similar estimates were also derived for univalent starlike functions and for univalent convex functions. We discuss and for close-to-convex functions such that , where h is an analytic function with a positive real part. Many coefficient problems, among others estimating of , or the Hankel determinants for close-to-convex functions or univalent functions, are not solved yet. Our results broaden the scope of theoretical results connected with these functionals defined for different subclasses of analytic univalent functions.
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Keywords:
coefficient problem; close-to-convex function; Fekete–Szegö functional; functional of Fekete–Szegö type
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MDPI and ACS Style
Tra̧bka-Wiȩcław, K.; Zaprawa, P.; Gregorczyk, M.; Rysak, A. On the Fekete–Szegö Type Functionals for Close-to-Convex Functions. Symmetry 2019, 11, 1497. https://doi.org/10.3390/sym11121497
AMA Style
Tra̧bka-Wiȩcław K, Zaprawa P, Gregorczyk M, Rysak A. On the Fekete–Szegö Type Functionals for Close-to-Convex Functions. Symmetry. 2019; 11(12):1497. https://doi.org/10.3390/sym11121497
Chicago/Turabian StyleTra̧bka-Wiȩcław, Katarzyna; Zaprawa, Paweł; Gregorczyk, Magdalena; Rysak, Andrzej. 2019. "On the Fekete–Szegö Type Functionals for Close-to-Convex Functions" Symmetry 11, no. 12: 1497. https://doi.org/10.3390/sym11121497
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