Proceedings of the Japan Academy, Series A, Mathematical Sciences

An extension of necessary and sufficient conditions for concave functions

Rintaro Ohno

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Abstract

In the present article we discuss necessary and sufficient conditions for concave functions, i.e. meromorphic functions which map the unit disk conformally on a domain whose complement is convex. The conditions will be given with respect to an arbitrary point $p\in (-1,1)$. We will also look at representation formulas for the related functions as well as an application of the derived formula.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 91, Number 1 (2015), 1-4.

Dates
First available in Project Euclid: 5 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.pja/1420466269

Digital Object Identifier
doi:10.3792/pjaa.91.1

Mathematical Reviews number (MathSciNet)
MR3296590

Zentralblatt MATH identifier
1317.30034

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

Keywords
Meromorphic univalent functions concave functions

Citation

Ohno, Rintaro. An extension of necessary and sufficient conditions for concave functions. Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 1, 1--4. doi:10.3792/pjaa.91.1. https://projecteuclid.org/euclid.pja/1420466269


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References

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