Vol. 57, No. 1, 1975

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Close-to-starlike holomorphic functions of several variables

John Pfaltzgraff and Ted Joe Suffridge

Vol. 57 (1975), No. 1, 271–279
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-tostarlike 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
Authors
John Pfaltzgraff
Ted Joe Suffridge