On functions satisfying more than one equation of Schiffer type

J. Macura; J. Śladkowska

Annales Polonici Mathematici (1993)

  • Volume: 58, Issue: 3, page 237-252
  • ISSN: 0066-2216

Abstract

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The paper concerns properties of holomorphic functions satisfying more than one equation of Schiffer type ( D n -equation). Such equations are satisfied, in particular, by functions that are extremal (in various classes of univalent functions) with respect to functionals depending on a finite number of coefficients.

How to cite

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J. Macura, and J. Śladkowska. "On functions satisfying more than one equation of Schiffer type." Annales Polonici Mathematici 58.3 (1993): 237-252. <http://eudml.org/doc/262393>.

@article{J1993,
abstract = {The paper concerns properties of holomorphic functions satisfying more than one equation of Schiffer type ($D_n$-equation). Such equations are satisfied, in particular, by functions that are extremal (in various classes of univalent functions) with respect to functionals depending on a finite number of coefficients.},
author = {J. Macura, J. Śladkowska},
journal = {Annales Polonici Mathematici},
keywords = {univalent function; coefficient region; Schiffer type equation; Bieberbach-Eilenberg function; Grunsky-Schah function},
language = {eng},
number = {3},
pages = {237-252},
title = {On functions satisfying more than one equation of Schiffer type},
url = {http://eudml.org/doc/262393},
volume = {58},
year = {1993},
}

TY - JOUR
AU - J. Macura
AU - J. Śladkowska
TI - On functions satisfying more than one equation of Schiffer type
JO - Annales Polonici Mathematici
PY - 1993
VL - 58
IS - 3
SP - 237
EP - 252
AB - The paper concerns properties of holomorphic functions satisfying more than one equation of Schiffer type ($D_n$-equation). Such equations are satisfied, in particular, by functions that are extremal (in various classes of univalent functions) with respect to functionals depending on a finite number of coefficients.
LA - eng
KW - univalent function; coefficient region; Schiffer type equation; Bieberbach-Eilenberg function; Grunsky-Schah function
UR - http://eudml.org/doc/262393
ER -

References

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  1. [1] A. K. Bahtin, Some properties of functions of class S, Ukrain. Mat. Zh. 33 (1981), 154-159 (in Russian); English transl.: Ukrainian Math. J. 33 (1981), 122-126. 
  2. [2] Y. Kubota, On extremal problems which correspond to algebraic univalent functions, Kodai Math. Sem. Rep. 25 (1973), 412-428. Zbl0278.30015
  3. [3] Z. J. Jakubowski and W. Majchrzak, On functions realizing the maximum of two functionals at a time, Serdica 10 (1984), 337-343. Zbl0576.30013
  4. [4] A. Rost and J. Śladkowska, Sur les fonctions de Bieberbach-Eilenberg satisfaisant à plus qu'une équation de type de Schiffer, Demonstratio Math., to appear. 
  5. [5] H. L. Royden, The coefficient problem for bounded schlicht functions, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 637-662. Zbl0041.40802
  6. [6] A. C. Schaeffer and D. C. Spencer, Coefficient Regions for Schlicht Functions, Amer. Math. Soc., 1950. Zbl0049.06003
  7. [7] J. Śladkowska, Sur les fonctions univalentes, bornées, satisfaisant deux au moins D n -équations, Demonstratio Math. 11 (1978), 1-28. Zbl0393.30011
  8. [8] V. V. Starkov, Bounded univalent functions realizing the extrema of two coefficients functionals at a time, in: Proc. XIth Instructional Conf. on the Theory of Extremal Problems, Łódź 1990, 31-33. 
  9. [9] K. Tochowicz, Functions which satisfy the differential equation of Schiffer type, Zeszyty Nauk. Politechn. Rzeszowskiej Mat. Fiz. 38 (6) (1987), 103-113. Zbl0684.34006

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