On coefficient inequalities in the Carathéodory class of functions

Adam Lecko

Annales Polonici Mathematici (2000)

  • Volume: 75, Issue: 1, page 59-67
  • ISSN: 0066-2216

Abstract

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Some inequalities are proved for coefficients of functions in the class P(α), where α ∈ [0,1), of functions with real part greater than α. In particular, new inequalities for coefficients in the Carathéodory class P(0) are given.

How to cite

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Lecko, Adam. "On coefficient inequalities in the Carathéodory class of functions." Annales Polonici Mathematici 75.1 (2000): 59-67. <http://eudml.org/doc/208384>.

@article{Lecko2000,
abstract = {Some inequalities are proved for coefficients of functions in the class P(α), where α ∈ [0,1), of functions with real part greater than α. In particular, new inequalities for coefficients in the Carathéodory class P(0) are given.},
author = {Lecko, Adam},
journal = {Annales Polonici Mathematici},
keywords = {Carathéodory class; coefficient inequalities},
language = {eng},
number = {1},
pages = {59-67},
title = {On coefficient inequalities in the Carathéodory class of functions},
url = {http://eudml.org/doc/208384},
volume = {75},
year = {2000},
}

TY - JOUR
AU - Lecko, Adam
TI - On coefficient inequalities in the Carathéodory class of functions
JO - Annales Polonici Mathematici
PY - 2000
VL - 75
IS - 1
SP - 59
EP - 67
AB - Some inequalities are proved for coefficients of functions in the class P(α), where α ∈ [0,1), of functions with real part greater than α. In particular, new inequalities for coefficients in the Carathéodory class P(0) are given.
LA - eng
KW - Carathéodory class; coefficient inequalities
UR - http://eudml.org/doc/208384
ER -

References

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  1. [1] C. Carathéodory, Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen, Math. Ann. 64 (1907), 95-115. Zbl38.0448.01
  2. [2] A. W. Goodman, Univalent Functions, Mariner, Tampa, FL 1983. 
  3. [3] Z. J. Jakubowski and J. Stankiewicz, On some classes of functions with the special normalizations, Folia Sci. Univ. Tech. Res. 73 (1990), 29-48. Zbl0747.30007
  4. [4] M. S. Robertson, On the theory of univalent functions, Ann. of Math. 37 (1936), 374-408. Zbl62.0373.05
  5. [5] M. S. Robertson, Univalent functions starlike with respect to a boundary point, J. Math. Anal. Appl. 81 (1981), 327-345. Zbl0472.30015

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