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

@inproceedings{Szynal2012OldAN,
  title={Old and new order of linear invariant family of harmonic mappings and the bound for Jacobian},
  author={Jan Szynal and Magdalena Sobczak-Kne{\'c} and Viktor V. Starkov},
  year={2012}
}
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. 1. A harmonic mapping f in the unit disk D = {z : |z| < 1} has a representation: (1.1) f(z) = h(z) + g(z) where h and g are holomorphic functions in D. We assume that f is locally univalent and sense-preserving… 
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