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Entire Functions with Some Derivatives Univalent

Published online by Cambridge University Press:  20 November 2018

S. M. Shah  and
S. Y. Trimble
S. M. Shah
Affiliation:
University of Kentucky, Lexington, Kentucky
S. Y. Trimble
Affiliation:
University of Missouri, Rolla, Missouri
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This paper is a continuation of the author's previous work, [6; 7], on the relationship between the radius of convergence of a power series and the number of derivatives of the power series which are univalent in a given disc.

In particular, let D be the open disc centered at 0, and let f be regular there. Suppose that is a strictly-increasing sequence of positive integers such that each f(np) is univalent in D. Let R be the radius of convergence of the power series, centered at 0, that represents f. In [7], we investigated the connection between R and . We showed that, in general

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 207 - 213
Copyright
Copyright © Canadian Mathematical Society 1974

References

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6. Shah, S. M. and Trimble, S. Y., Univalent functions with univalent derivatives, Bull. Amer. Math. Soc. 75 (1969), 153–157.Google Scholar
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