# On the Residuum of Concave Univalent Functions

• Volume: 32, Issue: 2-3, page 209-214
• ISSN: 1310-6600

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## Abstract

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2000 Mathematics Subject Classification: 30C25, 30C45.Let D denote the open unit disc and f:D→[C] be meromorphic and injective in D. We further assume that f has a simple pole at the point p О (0,1) and is normalized by f(0) = 0 and f′(0) = 1. In particular, we are concerned with f that map D onto a domain whose complement with respect to [C] is convex. Because of the shape of f(D) these functions will be called concave univalent functions with pole p and the family of these functions is denoted by Co(p). We determine for fixed p ∈ (0,1) the set of variability of the residuum of f, f ∈ Co(p).

## How to cite

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Wirths, K.-J.. "On the Residuum of Concave Univalent Functions." Serdica Mathematical Journal 32.2-3 (2006): 209-214. <http://eudml.org/doc/281507>.

@article{Wirths2006,
abstract = {2000 Mathematics Subject Classification: 30C25, 30C45.Let D denote the open unit disc and f:D→[C] be meromorphic and injective in D. We further assume that f has a simple pole at the point p О (0,1) and is normalized by f(0) = 0 and f′(0) = 1. In particular, we are concerned with f that map D onto a domain whose complement with respect to [C] is convex. Because of the shape of f(D) these functions will be called concave univalent functions with pole p and the family of these functions is denoted by Co(p). We determine for fixed p ∈ (0,1) the set of variability of the residuum of f, f ∈ Co(p).},
author = {Wirths, K.-J.},
journal = {Serdica Mathematical Journal},
keywords = {Concave Univalent Functions; Domain of Variability; Residuum; concave univalent function; domain of variability; residuum},
language = {eng},
number = {2-3},
pages = {209-214},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On the Residuum of Concave Univalent Functions},
url = {http://eudml.org/doc/281507},
volume = {32},
year = {2006},
}

TY - JOUR
AU - Wirths, K.-J.
TI - On the Residuum of Concave Univalent Functions
JO - Serdica Mathematical Journal
PY - 2006
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 32
IS - 2-3
SP - 209
EP - 214
AB - 2000 Mathematics Subject Classification: 30C25, 30C45.Let D denote the open unit disc and f:D→[C] be meromorphic and injective in D. We further assume that f has a simple pole at the point p О (0,1) and is normalized by f(0) = 0 and f′(0) = 1. In particular, we are concerned with f that map D onto a domain whose complement with respect to [C] is convex. Because of the shape of f(D) these functions will be called concave univalent functions with pole p and the family of these functions is denoted by Co(p). We determine for fixed p ∈ (0,1) the set of variability of the residuum of f, f ∈ Co(p).
LA - eng
KW - Concave Univalent Functions; Domain of Variability; Residuum; concave univalent function; domain of variability; residuum
UR - http://eudml.org/doc/281507
ER -

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