On a coefficient body for concave functions

Rintaro Ohno; Hiroshi Yanagihara

doi:10.1007/s40315-013-0018-y

On a coefficient body for concave functions

Rintaro Ohno, Hiroshi Yanagihara

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Abstract

For p ∈ (0, 1), let Co_p be the class of meromorphic and univalent functions f in the unit disk D with a simplepole at p such that ℂ\ f (D) is convex. These so-called concave functions can be expanded as. The present article shows a representation formula for functions of class Cop, using functions of positive real part, and gives an explicit description of the coefficient body {a₁(f), c_-1(f), c₁(f)}.

Original language	English
Pages (from-to)	237-251
Number of pages	15
Journal	Computational Methods and Function Theory
Volume	13
Issue number	2
DOIs	https://doi.org/10.1007/s40315-013-0018-y
Publication status	Published - 2013 Aug

Keywords

Concave functions
Univalent functions

ASJC Scopus subject areas

Analysis
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s40315-013-0018-y

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abstract = "For p ∈ (0, 1), let Cop be the class of meromorphic and univalent functions f in the unit disk D with a simplepole at p such that ℂ\ f (D) is convex. These so-called concave functions can be expanded as. The present article shows a representation formula for functions of class Cop, using functions of positive real part, and gives an explicit description of the coefficient body {a1(f), c-1(f), c1(f)}.",

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AU - Ohno, Rintaro

AU - Yanagihara, Hiroshi

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AB - For p ∈ (0, 1), let Cop be the class of meromorphic and univalent functions f in the unit disk D with a simplepole at p such that ℂ\ f (D) is convex. These so-called concave functions can be expanded as. The present article shows a representation formula for functions of class Cop, using functions of positive real part, and gives an explicit description of the coefficient body {a1(f), c-1(f), c1(f)}.

KW - Concave functions

KW - Univalent functions

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ER -

On a coefficient body for concave functions

Abstract

Keywords

ASJC Scopus subject areas

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