Old and new order of linear invariant family of harmonic mappings and the bound for Jacobian

• Autorzy: Magdalena Sobczak-Kneć , Viktor V. Starkov , Jan Szynal
• Języki publikacji: EN

Abstrakty

EN

The relation between the Jacobian and the orders of a linear invariant family of locally univalent harmonic mapping in the plane is studied. The new order (called the strong order) of a linear invariant family is defined and the relations between order and strong order are established.

Słowa kluczowe

EN

Planar harmonic mappings; order of a linear invariant family; Jacobian

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2011
• Tom: 65
• Numer: 2

Daty

wydano

2011

online

2016-07-27

Twórcy

autor

Magdalena Sobczak-Kneć

autor

Viktor V. Starkov

autor

Jan Szynal

Bibliografia

• Bshouty, D., Hengartner, W., Univalent harmonic mappings in the plane, Ann. Univ. Mariae Curie-Skłodowska Sect. A 48 (1994), 13-42.
• Duren, P., Harmonic Mappings in the Plane, Cambridge University Press, Cambridge, 2004.
• Godula, J., Liczberski, P. and Starkov, V. V., Order of linearly invariant mappings in Cn, Complex Variables Theory Appl. 42 (2000), 89-96.
• Pommerenke, Ch., Linear-invariante Familien analytischer Funktionen I, Math. Annalen 155 (1964), 108-154.
• Schaubroeck, L. E., Subordination of planar harmonic functions, Complex Variables Theory Appl. 41, (2000), 163-178.
• Sheil-Small, T., Constants for planar harmonic mappings, J. London Math. Soc. 42 (1990), 237-248.

Identyfikatory

DOI

10.17951/a.2011.65.2.191-202