PARABOLIC STARLIKE MAPPINGS OF THE UNIT BALL Bn

Let f be a locally univalent function on the unit disk U. We consider the normalized extensions of f to the Euclidean unit ball Bn Cn given by n;(f)(z) =( f(z1); ( f ′ (z1) ) ^z ) ; where 2 [0; 1=2], z = (z1; ^z) 2 Bn and n; (f)(z) = ( f(z1); ( f(z1) z1 ) ^z ) ; in which 2 [0; 1], f(z1) ̸= 0 and z = (z1; z) 2 Bn. In the case = 1=2, the function n; (f) reduces to the well known Roper-Su ridge extension operator. By using di erent methods, we prove that if fis parabolic starlike mapping on U then n; (f) and n; (f) are parabolic starlike mappings on Bn.