# On functions satisfying more than one equation of Schiffer type

Annales Polonici Mathematici (1993)

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

## Access Full Article

top## Abstract

top## How to cite

topJ. 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

top- [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] Y. Kubota, On extremal problems which correspond to algebraic univalent functions, Kodai Math. Sem. Rep. 25 (1973), 412-428. Zbl0278.30015
- [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] 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] H. L. Royden, The coefficient problem for bounded schlicht functions, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 637-662. Zbl0041.40802
- [6] A. C. Schaeffer and D. C. Spencer, Coefficient Regions for Schlicht Functions, Amer. Math. Soc., 1950. Zbl0049.06003
- [7] J. Śladkowska, Sur les fonctions univalentes, bornées, satisfaisant deux au moins ${D}_{n}$-équations, Demonstratio Math. 11 (1978), 1-28. Zbl0393.30011
- [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] K. Tochowicz, Functions which satisfy the differential equation of Schiffer type, Zeszyty Nauk. Politechn. Rzeszowskiej Mat. Fiz. 38 (6) (1987), 103-113. Zbl0684.34006

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.