Download PDF - On functions satisfying more than one equation of Schiffer typeAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

On functions satisfying more than one equation of Schiffer type

Authors 1, 1

Affiliations

  1. Institute of Mathematics, Silesian Technical University, Zwycięstwa 42, 44-100 Gliwice, Poland

Abstract

The paper concerns properties of holomorphic functions satisfying more than one equation of Schiffer type (Dn-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.

Keywords

ENG
univalent function, coefficient region, Schiffer type equation

Bibliography

  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.
  3. Z. J. Jakubowski and W. Majchrzak, On functions realizing the maximum of two functionals at a time, Serdica 10 (1984), 337-343.
  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.
  6. A. C. Schaeffer and D. C. Spencer, Coefficient Regions for Schlicht Functions, Amer. Math. Soc., 1950.
  7. J. Śladkowska, Sur les fonctions univalentes, bornées, satisfaisant deux au moins Dn-équations, Demonstratio Math. 11 (1978), 1-28.
  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.
Annales Polonici Mathematici
1993/58/3
Export to PBN, Opens in new tab
Pages:
237-252
Main language of publication
English
Received
1992-01-02
Accepted
1992-07-07
Published
1993
Exact and natural sciences