Treffer: Univalence of Derivatives of Functions Defined by Gap Power Series: Univalence of derivatives of functions defined by gap power series. II

Title:
Univalence of Derivatives of Functions Defined by Gap Power Series: Univalence of derivatives of functions defined by gap power series. II
Source:
Journal of the London Mathematical Society. :501-512
Publisher Information:
Wiley, 1975.
Publication Year:
1975
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
0024-6107
DOI:
10.1112/jlms/s2-9.3.501
DOI:
10.1016/0022-247x(76)90005-6
Rights:
Wiley Online Library User Agreement
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....1a9f9b3438bd09dff79c73c84c8c4370
Database:
OpenAIRE

Weitere Informationen

In this paper, we continue our work in [9] on the univalence of derivatives of functions defined by gap power series. We consider regular functions, f, defined in some region containing 0, and denote by pn and pJc> the radius of univalence and the radius of convexity, respectively, off@). For ease of notation, we shall sometimes write pn = p(n). Earlier, we considered functions defined by power series with gaps of at least a certain length. By that we meant the following: Suppose F(z) = Cj”=, Aizj. Then F is defined by a power series with gaps at least of length K provided that K is a nonnegative integer such that, if A, # 0 for some n, then Ancj = 0 for 1 < j < K. We proved the following [9].