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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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

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

First available in Project Euclid: 5 January 2015

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Zentralblatt MATH identifier

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

Meromorphic univalent functions concave functions


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.

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