On the univalent, bounded, non-vanishing and symmetric functions in the unit disk

J. Śladkowska

Annales Polonici Mathematici (1996)

  • Volume: 64, Issue: 3, page 291-299
  • ISSN: 0066-2216

Abstract

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The paper is devoted to a class of functions analytic, univalent, bounded and non-vanishing in the unit disk and in addition, symmetric with respect to the real axis. Variational formulas are derived and, as applications, estimates are given of the first and second coefficients in the considered class of functions.

How to cite

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J. Śladkowska. "On the univalent, bounded, non-vanishing and symmetric functions in the unit disk." Annales Polonici Mathematici 64.3 (1996): 291-299. <http://eudml.org/doc/269965>.

@article{J1996,
abstract = {The paper is devoted to a class of functions analytic, univalent, bounded and non-vanishing in the unit disk and in addition, symmetric with respect to the real axis. Variational formulas are derived and, as applications, estimates are given of the first and second coefficients in the considered class of functions.},
author = {J. Śladkowska},
journal = {Annales Polonici Mathematici},
keywords = {univalent function; variational method; Schiffer type equation; bounded univalent function; symmetric univalent function; variational methods; Schiffer-type equation},
language = {eng},
number = {3},
pages = {291-299},
title = {On the univalent, bounded, non-vanishing and symmetric functions in the unit disk},
url = {http://eudml.org/doc/269965},
volume = {64},
year = {1996},
}

TY - JOUR
AU - J. Śladkowska
TI - On the univalent, bounded, non-vanishing and symmetric functions in the unit disk
JO - Annales Polonici Mathematici
PY - 1996
VL - 64
IS - 3
SP - 291
EP - 299
AB - The paper is devoted to a class of functions analytic, univalent, bounded and non-vanishing in the unit disk and in addition, symmetric with respect to the real axis. Variational formulas are derived and, as applications, estimates are given of the first and second coefficients in the considered class of functions.
LA - eng
KW - univalent function; variational method; Schiffer type equation; bounded univalent function; symmetric univalent function; variational methods; Schiffer-type equation
UR - http://eudml.org/doc/269965
ER -

References

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  1. [1] G. M. Goluzin, Geometric Theory of a Complex Variable, Transl. Math. Monographs 26, Amer. Math. Soc., Providence, R.I., 1969. Zbl0183.07502
  2. [2] J. A. Hummel and B. Pinchuk, Variations for bounded nonvanishing univalent functions, J. Anal. Math. 44 (1984-85), 183-199. 
  3. [3] J. A. Hummel and M. M. Schiffer, Variational methods for Bieberbach-Eilenberg functions and for pairs, Ann. Acad. Sci. Fenn. Ser. AI Math. 3 (1977), 3-42. Zbl0379.30011
  4. [4] C. Pommerenke, Univalent Functions, Göttingen, 1975. 
  5. [5] D. V. Prokhorov and J. Szynal, Coefficient estimates for bounded nonvanishing functions, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981), 223-230. Zbl0469.30016
  6. [6] J. Śladkowska, Sur une famille des fonctions univalentes et bornées, Demonstratio Math. 22 (1989), 973-982. Zbl0712.30020
  7. [7] J. Śladkowska, Sur la famille des fonctions univalentes, bornées et symétriques qui n'atteignent pas une valeur fixée, Ann. Polon. Math. 52 (1990), 147-160. Zbl0718.30014
  8. [8] J. Śladkowska, A variational method for univalent nonvanishing functions in the unit disk, Folia Sci. Univ. Tech. Resov. 129, Math. 16 (1994), 63-77. Zbl0863.30031

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