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

Magdalena Sobczak-Kneć, Viktor V. Starkov, Jan Szynal

Abstract


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.

Keywords


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

Full Text:

PDF

References


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.




DOI: http://dx.doi.org/10.17951/a.2011.65.2.191-202
Data publikacji: 2016-07-27 21:54:13
Data złożenia artykułu: 2016-07-27 14:42:24

Refbacks

  • There are currently no refbacks.


Copyright (c) 2011 Magdalena Sobczak-Kneć, Viktor V. Starkov