In this paper, we obtain a distortion theorem of Jacobian matrix for biholomorphic subclasses of starlike mappings along a unit direction on the unit polydisc. These results extend the classical distortion theorem of starlike mappings to higher dimensions. We then give an upper bound estimate for biholomorphic subclasses of starlike mappings along a unit direction in a complex Banach space.
In this note,the author introduces some new subclasses of starlike mappings SΩn,p2,…,pn(β,A,B)={f ∈H(Ω):|itan β +(1-itan β)2/ρ(z)ρ/z(z)Jf-1(z)f(z)-1-AB/1-B2|
