Upper Bounds of the Third Hankel Determinant for Close-to-Convex Functions

In this paper, the third Hankel determinant for the class N of functions convex in one direction is estimated. An analogous problem is solved for a subclass of N consisting of functions with real coefficients. Additionally, this determinant for odd functions in N is estimated. Moreover, similar resu...

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Bibliographic Details
Published in:Symmetry (Basel) 2022-05, Vol.14 (5), p.885
Main Authors: Zaprawa, Paweł, Tra̧bka-Wiȩcław, Katarzyna
Format: Article
Language:English
Subjects:
close-to-convex functions
coefficients of analytic functions
Convex analysis
Inequality
Schwarz functions
third Hankel determinant
Upper bounds
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Summary:In this paper, the third Hankel determinant for the class N of functions convex in one direction is estimated. An analogous problem is solved for a subclass of N consisting of functions with real coefficients. Additionally, this determinant for odd functions in N is estimated. Moreover, similar results are obtained in the relative class M consisting of functions zf′(z), where f∈N. The majority of bounds is sharp.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14050885