Extension operators for locally univalent mappings
In the paper the following operators are studied \[ \Psi_{n, \alpha,\beta} (f)(z)=\left( f(z_1),\left( {f(z_1)\over z_1}\right)^\alpha \bigl( f(z_1)\bigr)^\beta z'\right),\;z\in B^n, \] where \(B^n=\{z\in \mathbb{C}^n:\|z \|<1\}\), \(z=(z_1,z')\), \(\alpha\geq 0\), \(\beta\geq 0\) and \(f\) is a locally univalent function on the unit disk, normalized by \(f(0)=f'(0)-1=0\), and such that \(f(z_1)\neq 0\), for \(z_1\neq 0\). Using these operators, the authors have generated linear-invariant families and investigate them.
scientific article; zbMATH DE number 1943208