Kyoto Journal of Mathematics

Coefficient estimates of analytic endomorphisms of the unit disk fixing a point with applications to concave functions

Rintaro Ohno and Toshiyuki Sugawa

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Abstract

In this article, we discuss the coefficient regions of analytic self-maps of the unit disk with a prescribed fixed point. As an application, we solve the Fekete–Szegő problem for normalized concave functions with a pole in the unit disk.

Article information

Source
Kyoto J. Math., Volume 58, Number 2 (2018), 227-241.

Dates
Received: 11 December 2015
Accepted: 17 June 2016
First available in Project Euclid: 9 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1496973623

Digital Object Identifier
doi:10.1215/21562261-2017-0015

Mathematical Reviews number (MathSciNet)
MR3799702

Zentralblatt MATH identifier
06896954

Subjects
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

Keywords
Fekete–Szegő problem fixed point concave functions variability region

Citation

Ohno, Rintaro; Sugawa, Toshiyuki. Coefficient estimates of analytic endomorphisms of the unit disk fixing a point with applications to concave functions. Kyoto J. Math. 58 (2018), no. 2, 227--241. doi:10.1215/21562261-2017-0015. https://projecteuclid.org/euclid.kjm/1496973623


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References

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