New characterization of strongly starlike mappings on balanced pseudoconvex domains in

In the paper there is continued a concept of strongly starlike mappings of order alpha on bounded balanced pseudoconvex domain with C 1 -plurisubharmonic defining function, introduced by H. Hamada, G. Kohr and M. Kohr. The main theorem contains two new geometric properties of such mappings and generalizes some one-dimensional results of W. Ma, D. Minda and T. Sugawa and an n-dimensional result given by the author.