On biholomorphic mappings in complex Banach spaces
The authors generalize the concept of mappings with \(g\)-parametric representation introduced by \textit{G. Kohr} in [Rev. Roum. Math. Pures Appl. 46, No. 6, 743--760 (2001; Zbl 1036.32014)] in the case of \(\mathbf{C}^n\) to biholomorphic normalized maps of the unit ball of any complex Banach space, giving rise to the classes \(\mathcal{M}_g\). They also extend the concept of strong starlikeness of order \(\alpha > 0\) to the Banach space setting for holomorphic maps defined on the unit ball in a natural manner. The main results are sharp growth estimates, distortion and covering theorems implying and unifying several known results concerning the classes \(\mathcal{ M}_g\) in extended form in infinite dimensions.
almost starlike mapping of order \(\alpha\)
strongly starlike mapping of order \(\alpha\)
scientific article; zbMATH DE number 5996742