Abstract

Universally prestarlike functions (of order a = 1) in the slit domain ? :=C\[1, 8] have recently been introduced in Ruscheweyh et al. (Israel J Math, to appear). This notation generalizes the corresponding one for functions in the unit disk D (and other circular domains in C). In this paper we study the behaviour of universally prestarlike functions under the Hadamard product. In particular it is shown that these function classes (with a fixed), are closed under convolution, and that their members, as Hadamard multipliers, also preserve the prestarlikeness (of the same order) of functions in arbitrary circular domains containing the origin. © Springer-Verlag 2008.