Extreme Points, Support Points and $$g$$ g -Loewner Chains Associated with Roper–Suffridge and Pfaltzgraff–Suffridge Extension Operators

Abstract

In this paper we are concerned with the generalized Pfaltzgraff–Suffridge extension operator \(\Psi _{n,\alpha }\), \(\alpha \ge 0\), that provides a way of extending a locally biholomorphic mapping \(f\in H(B^n)\) to a locally biholomorphic mapping \(F\in H(B^{n+1})\). We obtain a subordination preserving result under the operator \(\Psi _{n,\alpha }\) and we consider extreme and support points associated with this operator. In the end, we present some examples of \(g\)-starlike mappings, \(g\)-spirallike mappings of type \(\alpha \) and \(g\)-almost starlike mappings of order \(\alpha \) on \(B^n\) and we consider the preservation of these notions under certain Roper–Suffridge extension operators.