Faculty of Mathematics, Babes-Bolyai University, 1 M. Kogalniceanu
Str., 3400 Cluj-Napoca, Romania
e-mail: gkohr@math.ubbcluj.ro
Institute of Mathematics, Technical University of Lodz,
Av. Politechniki 11, 90-924 Lodz, Poland
e-mail: piliczb@ck-sg.p.lodz.pl
Abstract. In this paper, we will give the growth theorem of starlike mappings of order α on the unit ball B in complex Banach spaces. We also give an analytic sufficient condition for a locally biholomorphic mapping on B to be a starlike mapping of order α.
1991 Mathematics Subject Classification. 32A30, 32H02, 30C45.
Key words and phrases. Banach space, biholomorphic mappings, growth theorem, starlike mapping of order α.