A variational method for univalent functions connected with antigraphy

Janina Macura

Banach Center Publications (1996)

  • Volume: 37, Issue: 1, page 21-28
  • ISSN: 0137-6934

Abstract

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The paper is devoted to a class of functions analytic and univalent in the unit disk that are connected with an antigraphy e i φ ω ¯ + i ρ e i φ / 2 . Variational formulas and Grunsky inequalities are derived. As an application there are given some estimations in the considered class of functions.

How to cite

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Macura, Janina. "A variational method for univalent functions connected with antigraphy." Banach Center Publications 37.1 (1996): 21-28. <http://eudml.org/doc/208600>.

@article{Macura1996,
abstract = {The paper is devoted to a class of functions analytic and univalent in the unit disk that are connected with an antigraphy $e^\{iφ\}\bar\{ω\} + iρe^\{iφ/2\}$. Variational formulas and Grunsky inequalities are derived. As an application there are given some estimations in the considered class of functions.},
author = {Macura, Janina},
journal = {Banach Center Publications},
keywords = {Bieberbach-Eilenberg function},
language = {eng},
number = {1},
pages = {21-28},
title = {A variational method for univalent functions connected with antigraphy},
url = {http://eudml.org/doc/208600},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Macura, Janina
TI - A variational method for univalent functions connected with antigraphy
JO - Banach Center Publications
PY - 1996
VL - 37
IS - 1
SP - 21
EP - 28
AB - The paper is devoted to a class of functions analytic and univalent in the unit disk that are connected with an antigraphy $e^{iφ}\bar{ω} + iρe^{iφ/2}$. Variational formulas and Grunsky inequalities are derived. As an application there are given some estimations in the considered class of functions.
LA - eng
KW - Bieberbach-Eilenberg function
UR - http://eudml.org/doc/208600
ER -

References

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  1. [1] R. Caccioppoli, Sui funzionali lineari nel campo delle funzioni analitiche, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 13 (1931), 263-266. Zbl0002.03103
  2. [2] G. M. Goluzin, Geometričeskaya teorya funkcii kompleksnogo peremennogo, Moskwa 1966, 68-109, 157-158. 
  3. [3] H. Jondro, Sur une méthode variationnelle dans la famille des fonctions de Grunsky-Shah, Bull. Acad. Polon. Sci. 27 (1979), 541-547. Zbl0498.30023
  4. [4] H. Jondro, Les inégalités du type de Grunsky pour les fonctions de la classe K, Ann. Polon. Math. 45 (1985), 43-53. Zbl0581.30019
  5. [5] G. Schober, Univalent functions, Selected Topics, Lecture Notes in Mathematics 478, Springer-Verlag 1975. 

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