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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
7. Shah, S. M. and Trimble, S. Y., Univalent functions with univalent derivatives, III, J. Math. Mech. 19 (1969), 451–460.Google Scholar