Subclasses of biholomorphic mappings associated with g-Loewner chains on the unit ball in C~n

摘要

In this article,we use themethod of Loewner chains to generate certain subclasses of normalized biholomorphic mappings on the Euclidean unit ball B~n in C~n, which have interesting geometric characterizations. To this end, we obtain the characterization of g-starlike and g-spirallikemappings of type α ∈ (-π/2, π/2), as well as of g-almost starlike mappings of order α ∈ [0, 1), by using g-Loewner chains. Also, we will use these results to prove that, under certain assumptions, the mapping F(z) = P(z)z, z ∈ B~n, is g-starlike, g-spirallike of type α ∈ (-π/2, π/2) and g-almost starlike of order α ∈ [0, 1) on B~n, where P: B~n → C is a holomorphic function such that P(0) = 1. More generally, we consider conditions under which F has g-parametric representation on B~n. Various applications of these results are also provided.