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

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References


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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/10.2478/v10062-011-0024-3
Date of publication: 2016-07-27 21:54:13
Date of submission: 2016-07-27 14:42:24


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