Close-to-starlike holomorphic functions of several variables

John Pfaltzgraff and Ted Joe Suffridge

Vol. 57 (1975), No. 1, 271–279

DOI: 10.2140/pjm.1975.57.271

Abstract

Let X be a finite dimensional complex normed linear space with unit ball B = {x ∈ X : ∥x∥ < 1}. In this paper the notion of a close-to⋅starlike holomorphic mapping from B into X is defined. The definition is a direct generalization of W. Kaplan’s notion of one dimensional close-to-convex functions. It is shown that close-to-starlike mappings of B into X are univalent and these mappings are given an alternate characterization in terms of subordination chains.

Mathematical Subject Classification 2000

Primary: 32A10

Milestones

Received: 21 March 1974

Published: 1 March 1975