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Coefficient Estimates for a Class of Star-Like Functions

Published online by Cambridge University Press:  20 November 2018

D. A. Brannan ,
J. Clunie  and
W. E. Kirwan
D. A. Brannan
Affiliation:
Syracuse University, Syracuse, New York
J. Clunie
Affiliation:
Imperial College, London, England
W. E. Kirwan
Affiliation:
University of Maryland, College Park, Maryland
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In this note we continue the study, initiated in [1], of the class S*(α) of functions

(1.1)

that are analytic and univalent in the unit disc U and satisfy the condition

(1.2)

S*(1) is the frequently studied class of univalent star-like functions. For each α, S*(α) is a subclass of the class K(α) of close-to-convex functions of order α introduced by Pommerenke [4]. Properties of the class S*(α) proved useful in studying the coefficient behaviour of bounded univalent functions that are analytic and map U onto a convex domain [1]. In this note we investigate the problem of determining

but we are able to give only a partial solution.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 3 , 01 June 1970 , pp. 476 - 485
Copyright
Copyright © Canadian Mathematical Society 1970

References

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