# On the Residuum of Concave Univalent Functions

Serdica Mathematical Journal (2006)

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

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topWirths, 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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