Subclasses of biholomorphic mappings associated with g-Loewner chains on the unit ball in ℂn

Abstract

In this article, we use the method of Loewner chains to generate certain subclasses of normalized biholomorphic mappings on the Euclidean unit ball in , which have interesting geometric characterizations. To this end, we obtain the characterization of g-starlike and g-spirallike mappings of type , as well as of g-almost starlike mappings of order , by using g-Loewner chains. Also, we will use these results to prove that, under certain assumptions, the mapping , , is g-starlike, g-spirallike of type and g-almost starlike of order on , where is a holomorphic function such that . More generally, we consider conditions under which F has g-parametric representation on . Various applications of these results are also provided.