Loewner Chain Associated with the Modified Roper–Suffridge Extension Operator

Abstract

In this paper, we will determine under what condition the modified Roper–Suffridge extension operators F and \(\Psi _{n,\frac{1}{p_2},\ldots ,\frac{1}{p_n}}(f)\) can be embedded in a Loewner chain on the unit ball \(B^n\) and on a special bounded convex circular domain \(\Omega _{n,p_2,\ldots ,p_n}\), respectively. In particular, some well-known results can be obtained using the main theorems in this paper.